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1

A new Lagrangian dynamic reduction in field theory

For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.

François Gay-Balmaz; Tudor S. Ratiu

2014-07-01

2

Pictures and equations of motion in Lagrangian quantum field theory

The Heisenberg, interaction, and Schr\\"odinger pictures of motion are considered in Lagrangian (canonical) quantum field theory. The equations of motion (for state vectors and field operators) are derived for arbitrary Lagrangians which are polynomial or convergent power series in field operators and their first derivatives. The general links between different time-dependent pictures of motion are derived. It is pointed that all of them admit covariant formulation, similar to the one of interaction picture. A new picture, called the momentum picture, is proposed. It is a 4-dimensional analogue of the Schr\\"odinger picture of quantum mechanics as in it the state vectors are spacetime-dependent, while the field operators are constant relative to the spacetime. The equations of motion in momentum picture are derived and partially discussed. In particular, the ones for the field operators turn to be of algebraic type. The general idea of covariant pictures of motion is presented. The equations of motion in these pictures are derived.

Bozhidar Z. Iliev

2003-02-01

3

Peierls brackets in non-Lagrangian field theory

The concept of Lagrange structure allows one to systematically quantize the Lagrangian and non-Lagrangian dynamics within the path-integral approach. In this paper, I show that any Lagrange structure gives rise to a covariant Poisson brackets on the space of solutions to the classical equations of motion, be they Lagrangian or not. The brackets generalize the well-known Peierls' bracket construction and make a bridge between the path-integral and the deformation quantization of non-Lagrangian dynamics.

Sharapov, Alexey

2014-01-01

4

Peierls brackets in non-Lagrangian field theory

NASA Astrophysics Data System (ADS)

The concept of Lagrange structure allows one to systematically quantize the Lagrangian and non-Lagrangian dynamics within the path-integral approach. In this paper, I show that any Lagrange structure gives rise to a covariant Poisson bracket on the space of solutions to the classical equations of motion, be they Lagrangian or not. The bracket generalize the well-known Peierls' bracket construction and make a bridge between the path-integral and the deformation quantization of non-Lagrangian dynamics.

Sharapov, A. A.

2014-10-01

5

A study on relativistic lagrangian field theories with non-topological soliton solutions

We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call 'admissible' models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite-energy electrostatic spherically symmetric solutions which, unlike the (multi-) scalar case, are not always stable. The variational analysis of the energy functional leads now to supplementary restrictions to be imposed on the lagrangian densities in order to ensure the linear stability of the solitons. We establish a correspondence between any admissible soliton-supporting (multi-) scalar model and a family of admissible generalized gauge models supporting finite-energy electrostatic point-like solutions. Conversely, for each admissible soliton-supporting gauge-invariant model there is an associated unique admissible (multi-) scalar model with soliton solutions. This shows the exhaustive character of the admissibility and stability conditions in determining the class of soliton-supporting generalized gauge models. The usual Born-Infeld electrodynamic theory and its non-abelian extensions are shown to be (very particular) examples of one of these families.

Diaz-Alonso, J. [LUTH, Observatoire de Paris, CNRS, Universite Paris Diderot, 5 Place Jules Janssen, 92190 Meudon (France); Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias (Spain)], E-mail: joaquin.diaz@obspm.fr; Rubiera-Garcia, D. [Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias (Spain)

2009-04-15

6

NASA Technical Reports Server (NTRS)

To illustrate that a relativistic field theory need not be manifestly covariant, Lorentz-invariant Lagrangian densities are constructed that yield the equation satisfied by an interacting (two-component) Sakata-Taketani spin-0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric second-rank tensor, and a symmetric second-rank tensor, with the results specialized to electromagnetic interactions. For either of the two second-rank couplings, the equation is found to describe noncausal wave propagation, a property that is apparent from the dependence of the coefficients of the space derivatives on the external field; in contrast, the noncausality of the corresponding manifestly covariant Duffin-Kemmer-Petiau spin-0 equation is not so obvious. The possibilities for generalizing the results to higher spin theories involving only the essential 2(2J + 1) components for a particle with a definite spin J and mass m are discussed in considerable detail.

Guertin, R. F.; Wilson, T. L.

1977-01-01

7

Partition Function in One, Two and Three Spatial Dimensions from Effective Lagrangian Field Theory

The systematic effective Lagrangian method was first formulated in the context of the strong interaction: chiral perturbation theory (CHPT) is the effective theory of Quantum Chromodynamics (QCD). It was then pointed out that the method can be transferred to the nonrelativistic domain -- in particular, to describe the low-energy properties of ferromagnets. Interestingly, whereas for Lorentz-invariant systems the effective Lagrangian method fails in one spatial dimension ($d_s$=1), it perfectly works for nonrelativistic systems in $d_s$=1. In the present brief review, we give an outline of the method and then focus on the partition function for ferromagnetic spin chains, ferromagnetic films and ferromagnetic crystals up to three loops in the perturbative expansion -- an accuracy never achieved by conventional condensed matter methods. We then compare ferromagnets in $d_s$=1,2,3 with the behavior of QCD at low temperatures by considering the pressure and the order parameter. The two apparently very different sy...

Hofmann, Christoph P

2014-01-01

8

Partition Function in One, Two and Three Spatial Dimensions from Effective Lagrangian Field Theory

The systematic effective Lagrangian method was first formulated in the context of the strong interaction: chiral perturbation theory (CHPT) is the effective theory of Quantum Chromodynamics (QCD). It was then pointed out that the method can be transferred to the nonrelativistic domain -- in particular, to describe the low-energy properties of ferromagnets. Interestingly, whereas for Lorentz-invariant systems the effective Lagrangian method fails in one spatial dimension ($d_s$=1), it perfectly works for nonrelativistic systems in $d_s$=1. In the present brief review, we give an outline of the method and then focus on the partition function for ferromagnetic spin chains, ferromagnetic films and ferromagnetic crystals up to three loops in the perturbative expansion -- an accuracy never achieved by conventional condensed matter methods. We then compare ferromagnets in $d_s$=1,2,3 with the behavior of QCD at low temperatures by considering the pressure and the order parameter. The two apparently very different systems (ferromagnets and QCD) are related from a universal point of view based on the spontaneously broken symmetry. In either case, the low-energy dynamics is described by an effective theory containing Goldstone bosons as basic degrees of freedom.

Christoph P. Hofmann

2014-02-04

9

Grassmann-graded Lagrangian theory of even and odd variables

Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems, characterized by hierarchies of non-trivial higher-order Noether identities and gauge symmetries. This is a general case of classical field theory and Lagrangian non-relativistic mechanics.

G. Sardanashvily

2012-06-12

10

The Heisenberg-Euler Lagrangian as an example of an effective field theory

NASA Astrophysics Data System (ADS)

We review the beginning of the effective Lagrangian in QED that was first introduced in the literature by W. Heisenberg and H. Euler in 1936. Deviating from their way of calculating the one-loop effective correction to the classical Maxwell Lagrangian, we use Green's functions and adopt the Fock-Schwinger proper-time method. The important role of the Heisenberg-Euler effective Lagrangian is explicitly demonstrated for low-energy photon-photon processes.

Dittrich, Walter

2014-10-01

11

Lagrangian formalism for tensor fields

The Lagrangian formalism for tensor fields over differentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and metrics [$(\\bar{L}_n,g)$-spaces] is considered. The functional variation and the Lie variation of a Lagrangian density, depending on components of tensor fields (with finite rank) and their first and second covariant derivatives are established. A variation operator is determined and the corollaries of its commutation relations with the covariant and the Lie differential operators are found. The canonical (common) method of Lagrangians with partial derivatives (MLPD) and the method of Lagrangians with covariant derivatives (MLCD) are outlined. They differ from each other by the commutation relations the variation operator has to obey with the covariant and the Lie differential operator. The canonical and covariant Euler-Lagrange equations are found as well as their corresponding $(\\bar{L}_n,g)$-spaces. The energy-momentum tensors are considered on the basis of the Lie variation and the covariant Noether identities.

S. Manoff

2000-07-21

12

Fibre Bundles, Jet Manifolds and Lagrangian Theory. Lectures for Theoreticians

In contrast with QFT, classical field theory can be formulated in a strict mathematical way by treating classical fields as sections of smooth fibre bundles. Addressing to the theoreticians, these Lectures aim to compile the relevant material on fibre bundles, jet manifolds, connections, graded manifolds and Lagrangian theory. They follow the perennial course of lectures on geometric methods in field theory at the Department of Theoretical Physics of Moscow State University.

G. Sardanashvily

2009-08-13

13

Higher--Order Lagrangian Perturbation Theory

Fundamental assumptions which form the basis of models for large-scale structure in the Universe are sketched in light of a Lagrangian description of inhomogeneities. This description is introduced for Newtonian self-gravitating flows. On its basis a Lagrangian perturbation approach is discussed and compared with the standard Eulerian theory of gravitational instability. The performance of Lagrangian perturbation solutions up to the third order is demonstrated in comparison with numerical N-body simulations. First results of this comparison are presented for large scales (PM-code) and for small scales (tree-code).

T. Buchert

1994-03-11

14

Using Lagrangian perturbation theory for precision cosmology

The evolution of dark matter fluctuations can be described as a global coordinate transformation caused by long-wavelength displacement vector acting on short-wavelength modes undergoing non-linear growth. The long-wavelength displacement vector does not ever contribute to the non-linear power spectrum because of the cancellation of the global coordinate transformation due to the translation symmetry in the ensemble average. Unlike other perturbation approaches, the standard perturbation theory and the Lagrangian perturbation theory naturally exclude the unphysical effects from the long-wavelength displacement vector and focus the short-wavelength modes. In this paper, we explore the Lagrangian perturbation theory at 1-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum in the Lagrangian perturbation theory only with the contributions from the short-wavelength modes. Our approximate solution has good convergence in the series of the expansion...

Sugiyama, Naonori S

2013-01-01

15

Effective Lagrangian in the type-I superstring theory

The leading terms in the tree-level effective Lagrangian for the vector gauge field in the theory of open superstrings are obtained by analysis of the three- and four-particle tree amplitudes on the mass shell. The path integral formalism is used to find a closed expression for terms of any order in ' which depend only on the strength of the

Tsei-brevetlin

1987-01-01

16

Functional Determinants in Higher Derivative Lagrangian Theories

Motivated by the considerable success of alternative theories of gravity, we consider the toy model of a higher derivative Lagrangian theory, namely the Pais-Uhlenbeck oscillator studied in a recent paper by Hawking-Hertog. Its Euclidean Path Integral is studied with a certain detail and a pedagogical derivation of the propagator, which makes use of a Theorem due to Forman, is consequently proposed

Roberto Di Criscienzo; Sergio Zerbini

2009-07-24

17

Covariant Hamiltonian field theory. Path integral quantization

The Hamiltonian counterpart of classical Lagrangian field theory is covariant Hamiltonian field theory where momenta correspond to derivatives of fields with respect to all world coordinates. In particular, classical Lagrangian and covariant Hamiltonian field theories are equivalent in the case of a hyperregular Lagrangian, and they are quasi-equivalent if a Lagrangian is almost-regular. In order to quantize covariant Hamiltonian field theory, one usually attempts to construct and quantize a multisymplectic generalization of the Poisson bracket. In the present work, the path integral quantization of covariant Hamiltonian field theory is suggested. We use the fact that a covariant Hamiltonian field system is equivalent to a certain Lagrangian system on a phase space which is quantized in the framework of perturbative field theory. We show that, in the case of almost-regular quadratic Lagrangians, path integral quantizations of associated Lagrangian and Hamiltonian field theories are equivalent.

D. Bashkirov; G. Sardanashvily

2004-02-06

18

By using path integral techniques nuclear field theory (NFT) is developed for Fermi systems interacting via a general two-body force. The NFT Lagrangian is strictly derived. As a by-product, the corresponding graphical rules are obtained. The relation between the NFT and the conventional Feynman diagrammatic many-body perturbation theory is established for processes connecting initial and final states, too.

H. Reinhardt

1978-01-01

19

Reconstructing baryon oscillations: A Lagrangian theory perspective

Recently Eisenstein and collaborators introduced a method to 'reconstruct' the linear power spectrum from a nonlinearly evolved galaxy distribution in order to improve precision in measurements of baryon acoustic oscillations. We reformulate this method within the Lagrangian picture of structure formation, to better understand what such a method does, and what the resulting power spectra are. We show that reconstruction does not reproduce the linear density field, at second order. We however show that it does reduce the damping of the oscillations due to nonlinear structure formation, explaining the improvements seen in simulations. Our results suggest that the reconstructed power spectrum is potentially better modeled as the sum of three different power spectra, each dominating over different wavelength ranges and with different nonlinear damping terms. Finally, we also show that reconstruction reduces the mode-coupling term in the power spectrum, explaining why miscalibrations of the acoustic scale are reduced when one considers the reconstructed power spectrum.

Padmanabhan, Nikhil [Physics Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720 (United States); White, Martin [Departments of Physics and Astronomy, 601 Campbell Hall, University of California, Berkeley, California 94720 (United States); Cohn, J. D. [Space Sciences Laboratory, 601 Campbell Hall, University of California, Berkeley, California, 94720 (United States)

2009-03-15

20

Topics in low-dimensional field theory

Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.

Crescimanno, M.J.

1991-04-30

21

String perturbation theory and effective Lagrangians

We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with 'tadpole' divergences in the effective field theory with a cosmological term, which also contains an effective potential for the dilation. Also, corrections to ..beta..-functions are compared with variations of the effective action. In both cases we find an inconsistency between the two. This is a serious problem which could undermine our ability to remove divergences from the bosonic string.

Klebanov, I.

1987-09-01

22

Renormalization and quantum field theory

The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need not exist a canonical Feynman measure, there is a canonical orbit of Feynman measures under renormalization. We then construct a perturbative quantum field theory from a Lagrangian and a Feynman measure, and show that it satisfies perturbative analogues of the Wightman axioms, extended to allow time-ordered composite operators over curved spacetimes.

R. E. Borcherds

2010-07-31

23

Effective metric Lagrangians from an underlying theory with two propagating degrees of freedom

We describe an infinite-parametric class of effective metric Lagrangians that arise from an underlying theory with two propagating degrees of freedom. The Lagrangians start with the Einstein-Hilbert term, continue with the standard R{sup 2}, (Ricci){sup 2} terms, and in the next order contain (Riemann){sup 3} as well as on-shell vanishing terms. This is exactly the structure of the effective metric Lagrangian that renormalizes quantum gravity divergences at two loops. This shows that the theory underlying the effective field theory of gravity may have no more degrees of freedom than is already contained in general relativity. We show that the reason why an effective metric theory may describe just two propagating degrees of freedom is that there exists a (nonlocal) field redefinition that maps an infinitely complicated effective metric Lagrangian to the usual Einstein-Hilbert one. We describe this map for our class of theories and, in particular, exhibit it explicitly for the (Riemann){sup 3} term.

Krasnov, Kirill [School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)

2010-04-15

24

NASA Astrophysics Data System (ADS)

Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low ultraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term which is quadratic in the fields, and physical predictions can be read straight from the effective Lagrangian. Methods will be discussed how to compute an effective low energy action from a given fundamental action, either analytically or numerically, or by a combination of both methods. Basically, the idea is to integrate out the high frequency components of fields. This requires the choice of a "blockspin", i.e. the specification of a low frequency field as a function of the fundamental fields. These blockspins will be the fields of the effective field theory. The blockspin needs not be a field of the same type as one of the fundamental fields, and it may be composite. Special features of blockspins in nonabelian gauge theories will be discussed in some detail. In analytical work and in multigrid updating schemes one needs interpolation kernels A from coarse to fine grid in addition to the averaging kernels C which determines the blockspin. A neural net strategy for finding optimal kernels is presented. Numerical methods are applicable to obtain actions of effective theories on lattices of finite volume. The special case of a "lattice" with a single site (the constraint effective potential) is of particular interest. In a Higgs model, the effective action reduces in this case to the free energy, considered as a function of a gauge covariant magnetization. Its shape determines the phase structure of the theory. Its loop expansion with and without gauge fields can be used to determine finite size corrections to numerical data.

Mack, G.; Kalkreuter, T.; Palma, G.; Speh, M.

25

Cosmological structure formation with augmented Lagrangian perturbation theory

NASA Astrophysics Data System (ADS)

We present a new fast and efficient approach to model structure formation with augmented Lagrangian perturbation theory (ALPT). Our method is based on splitting the displacement field into a long- and a short-range component. The long-range component is computed by second-order LPT (2LPT). This approximation contains a tidal non-local and non-linear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low-density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zel'dovich approximation). We propose to combine both approximations using for the short-range displacement field the SC solution. A Gaussian filter with a smoothing radius rS is used to separate between both regimes. We use the result of 25 dark-matter-only N-body simulations to benchmark at z = 0 the different approximations: first-, second-, third-order LPT, SC and our novel combined ALPT model. This comparison demonstrates that our method improves previous approximations at all scales showing ˜25 and ˜75 per cent higher correlation than 2LPT with the N-body solution at k = 1 and 2 h Mpc-1, respectively. We conduct a parameter study to determine the optimal range of smoothing radii and find that the maximum correlation is achieved with rS = 4-5 h-1 Mpc. This structure formation approach could be used for various purposes, such as setting-up initial conditions for N-body simulations, generating mock galaxy catalogues, cosmic web analysis or for reconstructions of the primordial density fluctuations.

Kitaura, Francisco-Shu; Heß, Steffen

2013-08-01

26

Quantum noncanonical field theory: Symmetries and interaction

The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincare invariance in an auxiliary spacetime is found in the Lagrangian version of the path integral formulation. This invariance is contrasted with the idea of doubly (or deformed) special relativity. This analysis is then used to go from the free theory of a complex field to an interacting field theory.

Carmona, J. M.; Cortes, J. L.; Indurain, J.; Mazon, D. [Departamento de Fisica Teorica, Universidad de Zaragoza, Zaragoza 50009 (Spain)

2009-11-15

27

We analyze the conditions of the electromagnetic potentials for systems with electric and magnetic charges and the Lagrangian theory with these potentials. The constructed Lagrangian function is valid for obtaining the field equations and the extended Lorentz force for dyonic charges for both relativistic particles in vacuum and non-relativistic entities in solids. In a second part, with the one-body Hamiltonian of independent particles in external fields, we explore some dual properties of the dyonic system under external fields. We analyze the possible diamagnetic (and 'diaelectric') response of magnetic monopoles under a weak and constant electromagnetic field and the theory of Landau levels in the case of magnetic charges under strong electromagnetic constant fields. - Highlights: Black-Right-Pointing-Pointer We study the Lagrangian formalism for magnetic charges. Black-Right-Pointing-Pointer We analyze the electromagnetic potentials for dyons. Black-Right-Pointing-Pointer We study two dual properties of solid systems with magnetic charges. Black-Right-Pointing-Pointer A quantum study of solids with monopoles under electromagnetic constant fields.

Costa-Quintana, J., E-mail: joan.costa@uab.cat; Lopez-Aguilar, F., E-mail: fernando.lopez@uab.cat

2012-08-15

28

Effective Lagrangians and Field Algebras with Chiral Symmetry

This paper reviews recent developments of effective Lagrangians and field algebras as means of treating chiral symmetry and partially conserved axial current (PCAC) for the study of elementary particle physics. The techniques employed are developed in considerable detail. As examples, we concentrate primarily on spin 0 and 1, linear and nonlinear realizations of SU(2)×SU(2) and SU(3)×SU(3) and some of the

S. Gasiorowicz; D. A. Geffen

1969-01-01

29

Augmented Lagrangian formulation of orbital-free density functional theory

NASA Astrophysics Data System (ADS)

We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas-Fermi-von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.

Suryanarayana, Phanish; Phanish, Deepa

2014-10-01

30

NASA Astrophysics Data System (ADS)

Preface for students; Preface for instructors; Acknowledgements; Part I. Spin Zero: 1. Attempts at relativistic quantum mechanics; 2. Lorentz invariance; 3. Canonical quantization of scalar fields; 4. The spin-statistics theorem; 5. The LSZ reduction formula; 6. Path integrals in quantum mechanics; 7. The path integral for the harmonic oscillator; 8. The path integral for free field theory; 9. The path integral for interacting field theory; 10. Scattering amplitudes and the Feynman rules; 11. Cross sections and decay rates; 12. Dimensional analysis with ?=c=1; 13. The Lehmann-Källén form; 14. Loop corrections to the propagator; 15. The one-loop correction in Lehmann-Källén form; 16. Loop corrections to the vertex; 17. Other 1PI vertices; 18. Higher-order corrections and renormalizability; 19. Perturbation theory to all orders; 20. Two-particle elastic scattering at one loop; 21. The quantum action; 22. Continuous symmetries and conserved currents; 23. Discrete symmetries: P, T, C, and Z; 24. Nonabelian symmetries; 25. Unstable particles and resonances; 26. Infrared divergences; 27. Other renormalization schemes; 28. The renormalization group; 29. Effective field theory; 30. Spontaneous symmetry breaking; 31. Broken symmetry and loop corrections; 32. Spontaneous breaking of continuous symmetries; Part II. Spin One Half: 33. Representations of the Lorentz Group; 34. Left- and right-handed spinor fields; 35. Manipulating spinor indices; 36. Lagrangians for spinor fields; 37. Canonical quantization of spinor fields I; 38. Spinor technology; 39. Canonical quantization of spinor fields II; 40. Parity, time reversal, and charge conjugation; 41. LSZ reduction for spin-one-half particles; 42. The free fermion propagator; 43. The path integral for fermion fields; 44. Formal development of fermionic path integrals; 45. The Feynman rules for Dirac fields; 46. Spin sums; 47. Gamma matrix technology; 48. Spin-averaged cross sections; 49. The Feynman rules for majorana fields; 50. Massless particles and spinor helicity; 51. Loop corrections in Yukawa theory; 52. Beta functions in Yukawa theory; 53. Functional determinants; Part III. Spin One: 54. Maxwell's equations; 55. Electrodynamics in coulomb gauge; 56. LSZ reduction for photons; 57. The path integral for photons; 58. Spinor electrodynamics; 59. Scattering in spinor electrodynamics; 60. Spinor helicity for spinor electrodynamics; 61. Scalar electrodynamics; 62. Loop corrections in spinor electrodynamics; 63. The vertex function in spinor electrodynamics; 64. The magnetic moment of the electron; 65. Loop corrections in scalar electrodynamics; 66. Beta functions in quantum electrodynamics; 67. Ward identities in quantum electrodynamics I; 68. Ward identities in quantum electrodynamics II; 69. Nonabelian gauge theory; 70. Group representations; 71. The path integral for nonabelian gauge theory; 72. The Feynman rules for nonabelian gauge theory; 73. The beta function for nonabelian gauge theory; 74. BRST symmetry; 75. Chiral gauge theories and anomalies; 76. Anomalies in global symmetries; 77. Anomalies and the path integral for fermions; 78. Background field gauge; 79. Gervais-Neveu gauge; 80. The Feynman rules for N x N matrix fields; 81. Scattering in quantum chromodynamics; 82. Wilson loops, lattice theory, and confinement; 83. Chiral symmetry breaking; 84. Spontaneous breaking of gauge symmetries; 85. Spontaneously broken abelian gauge theory; 86. Spontaneously broken nonabelian gauge theory; 87. The standard model: Gauge and Higgs sector; 88. The standard model: Lepton sector; 89. The standard model: Quark sector; 90. Electroweak interactions of hadrons; 91. Neutrino masses; 92. Solitons and monopoles; 93. Instantons and theta vacua; 94. Quarks and theta vacua; 95. Supersymmetry; 96. The minimal supersymmetric standard model; 97. Grand unification; Bibliography.

Srednicki, Mark

2007-01-01

31

Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation

We present a simple method to derive the semiclassical equations of motion for a spinning particle in a gravitational field. We investigate the cases of classical, rotating particles (pole-dipole particles), as well as particles with intrinsic spin. We show that, starting with a simple Lagrangian, one can derive equations for the spin evolution and momentum propagation in the framework of metric theories of gravity and in theories based on a Riemann-Cartan geometry (Poincare gauge theory), without explicitly referring to matter current densities (spin and energy-momentum). Our results agree with those derived from the multipole expansion of the current densities by the conventional Papapetrou method and from the WKB analysis for elementary particles.

M. Leclerc

2005-05-04

32

Effective Field Theory and Heavy Quark Physics

These notes are based on five lectures presented at the 2004 Theoretical Advanced Study Institute (TASI) on ``Physics in D>=4''. After a brief motivation of flavor physics, they provide a pedagogical introduction to effective field theory, the effective weak Lagrangian, and the technology of renormalization-group improved perturbation theory. These general methods are then applied in the context of heavy-quarks physics, introducing the concepts of heavy-quark and soft-collinear effective theory.

Matthias Neubert

2005-12-17

33

A Lagrangian theory of the classical spinning electron

NASA Technical Reports Server (NTRS)

A Lagrangian is defined that governs the dynamics of a classical electron with spin, moving under the influence of electromagnetic forces. The Euler-Lagrange equations associated with this Lagrangian for space-time position x exp-alpha provide a generalization of the Lorentz force law. The remaining Euler-Lagrange equations lead directly to the (generalized) Frenkel (1926)-Thomas (1927)-BMT (1959) equations.

Nash, P. L.

1984-01-01

34

About non standard Lagrangians in cosmology

A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.

Dimitrijevic, Dragoljub D.; Milosevic, Milan [Department of Physics, Faculty of Science and Mathematics, University of Nis, Visegradska 33, P.O. Box 224, 18000 Nis (Serbia)

2012-08-17

35

Exponential Lagrangian for the Gravitational Field and the problem of Vacuum Energy

We will analyze two particular features of an exponential gravitational Lagrangian. On the one hand, while this choice of the Lagrangian density allows for two free parameters, only one scale, the cosmological constant, arises as fundamental when the proper Einsteinian limit is to be recovered. On the other hand, the vacuum energy arising from $f(R)$ theories such that $f(0)\

O. M. Lecian; G. Montani

2008-03-11

36

Introduction Classical Field Theory

Introduction Classical Field Theory Locally Covariant Quantum Field Theory Renormalization Time evolution Conclusions and outlook Locality and Algebraic Structures in Field Theory Klaus Fredenhagen IIÂ¨utsch and Pedro Lauridsen Ribeiro) Klaus Fredenhagen Locality and Algebraic Structures in Field Theory #12

Baer, Christian

37

Electromagnetic Field Theory BO THIDÃ? UPSILON BOOKS #12;#12;ELECTROMAGNETIC FIELD THEORY #12;#12;Electromagnetic Field Theory BO THIDÃ? Swedish Institute of Space Physics and Department of Astronomy and Space, Sweden UPSILON BOOKS Â· COMMUNA AB Â· UPPSALA Â· SWEDEN #12;Also available ELECTROMAGNETIC FIELD THEORY

Hart, Gus

38

Species doubling and effective Lagrangians

Coupling gauge fields to the chiral currents from an effective Lagrangian for pseudoscalar mesons naturally gives rise to a species doubling phenomenon similar to that seen with fermionic fields in lattice gauge theory.

Michael Creutz; Michel Tytgat

1996-08-02

39

Species Doubling and Chiral Lagrangians

Coupling gauge fields to the chiral currents from an effective Lagrangian for pseudoscalar mesons naturally gives rise to a species doubling phenomenon similar to that seen with fermionic fields in lattice gauge theory.

Michael Creutz; Michel Tytgat

1996-05-15

40

Modified Ostrogradski formulation of field theory

We present a method for the Hamiltonian formulation of field theories that are based on Lagrangians containing second derivatives. The new feature of our formalism is that all four partial derivatives of the field variables are initially considered as independent fields, in contrast to the conventional Ostrogradski method, where only the velocity is turned into an independent field variable. The consistency of the formalism is demonstrated by simple unconstrained and constrained second order scalar field theories. Its application to General Relativity is briefly outlined.

M. Leclerc

2006-10-07

41

Quantum Field Theory, Revised Edition

NASA Astrophysics Data System (ADS)

Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical interpretation is stressed at every point and its use is illustrated in detailed applications. After studying this book, the reader should be able to calculate any process in lowest order of perturbation theory for both QED and the standard electro-weak theory, and in addition, calculate lowest order radiative corrections in QED using the powerful technique of dimensional regularization. Contents: Preface; 1 Photons and electromagnetic field; 2 Lagrangian field theory; 3 The Klein--Gordon field; 4 The Dirac field; 5 Photons: covariant theory; 6 The S-matrix expansion; 7 Feynman diagrams and rules in QED; 8 QED processes in lowest order; 9 Radiative corrections; 10 Regularization; 11 Weak interactions; 13 Spontaneous symmetry breaking; 14 The standard electro-weak theory; Appendix A The Dirac equation; Appendix B Feynman rules and formulae for perturbation theory; Index.

Mandl, F.; Shaw, G.

1994-01-01

42

Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.

Kheirandish, F.; Amooshahi, M. [Department of Physics, University of Isfahan, Isfahan (Iran, Islamic Republic of)

2008-11-18

43

On background-independent open-string field theory

A framework for background-independent open-string field theory is proposed. The approach involves using the Batalin-Vilkovisky formalism, in a way suggested by recent developments in closed-string field theory, to implicitly define a gauge-invariant Lagrangian in a hypothetical ``space of all open-string world-sheet theories.'' It is built into the formalism that classical solutions of the string field theory are Becchi-Rouet-Stora-Tyutin- (BRST-) invariant

Edward Witten

1992-01-01

44

Chiral Effective Theory with a Scalar Field

We report on an extension of Chiral Perturbation Theory including a scalar, isosiglet field [1](henceforth refered as {chi}PT{sub S}). We work out the chiral Lagrangian up to next-to-leading order (NLO) including the new field and present the expressions for the pion mass and the pion decay constant computed in this new theory, which feature distincly new analytical structure on the quark mass. We compare the new expressions and the standard Chiral Perturbation Theory ones with lattice data, and provide the values for the low energy constants obtained.

Tarrus, Jaume [Departament d'Estructura i Constituents de la Materia and Institut de Ciencies del Cosmos, Universitat de Barcelona (Spain); Diagonal, 647, E-08028 Barcelona, Catalonia (Spain)

2011-05-23

45

On exact tachyon potential in open string field theory

In these notes we revisit the tachyon lagrangian in the open string field theory using background independent approach of Witten from 1992. We claim that the tree level lagrangian (up to second order in derivatives and modulo some class of field redefinitions) is given by L = e-T(partialT)2+(1+T)e-T. Upon obvious change of variables this leads to the potential energy -phi2log

Anton A. Gerasimov; Samson L. Shatashvili

2000-01-01

46

The Lagrangian formulation of strong-field quantum electrodynamics in a plasma

NASA Astrophysics Data System (ADS)

The Lagrangian formulation of the scalar and spinor quantum electrodynamics in the presence of strong laser fields in a plasma medium is considered. We include the plasma influence in the free Lagrangian analogously to the "Furry picture" and obtain coupled equations of motion for the plasma particles and for the laser propagation. We demonstrate that the strong-field wave (i.e., the laser) satisfies a massive dispersion relation and obtain self-consistently the effective mass of the laser photons. The Lagrangian formulation derived in this paper is the basis for the cross sections calculation of quantum processes taking place in the presence of a plasma.

Raicher, Erez; Eliezer, Shalom; Zigler, Arie

2014-05-01

47

NASA Astrophysics Data System (ADS)

The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and then, on more involved nonlocal theories (colored and noncolored) defined over a tensor product of the same group, we address the issue of translation and dilatation symmetries and the corresponding Noether theorem. The energy momentum tensor and dilatation current are derived and their properties identified for each case.

Ben Geloun, Joseph

2012-02-01

48

Lagrangian formulations for Bose and Fermi higher-spin fields of mixed symmetry

We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting and then the ($\\g$-)trace constraints on fields and gauge parameters are eliminated via the introduction of a number of auxiliary fields.

Andrea Campoleoni

2009-05-10

49

Quantum Field Theory and Representation Theory

Quantum Field Theory and Representation Theory Peter Woit woit@math.columbia.edu Department of Mathematics Columbia University Quantum Field Theory and Representation Theory Â p.1 #12;Outline of the talk Â· Quantum Mechanics and Representation Theory: Some History Quantum Field Theory and Representation Theory

Woit, Peter

50

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory

Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches.

Andreussi, T. [Alta S.p.A., Pisa 56121 (Italy)] [Alta S.p.A., Pisa 56121 (Italy); Morrison, P. J. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1060 (United States)] [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1060 (United States); Pegoraro, F. [Università di Pisa, Dipartimento di Fisica E. Fermi, Pisa 56127 (Italy)] [Università di Pisa, Dipartimento di Fisica E. Fermi, Pisa 56127 (Italy)

2013-09-15

51

Hall viscosity from effective field theory

For two-dimensional non-dissipative fluids with broken parity, we show via effective field theory methods that the infrared dynamics generically exhibit Hall viscosity--a conservative form of viscosity compatible with two-dimensional isotropy. The equality between the Hall viscosity coefficient and the ground state's intrinsic angular momentum density follows straightforwardly from their descending from the same Lagrangian term of the low-energy effective action.

Alberto Nicolis; Dam Thanh Son

2011-01-01

52

Soliton solutions in relativistic field theories and gravitation

We report on some recent results on a class of relativistic lagrangian field theories supporting non-topological soliton solutions and their applications in the contexts of Gravitation and Cosmology. We analyze one and many-components scalar fields and gauge fields.

Joaquin Diaz-Alonso; Diego Rubiera-Garcia

2007-12-11

53

Tulczyjew Triples in Higher Derivative Field Theory

The geometrical structure known as Tulczyjew triple has been used with success in analytical mechanics and first order field theory to describe a wide range of physical systems including Lagrangian/Hamiltonian systems with constraints and/or sources, or with singular Lagrangian. Starting from the first principles of the variational calculus we derive Tulczyjew triples for classical field theories of arbitrary high order, i.e.~depending on arbitrary high derivatives of the fields. A first triple appears as the result of considering higher order theories as first order ones with configurations being constrained to be holonomic jets. A second triple is obtained after a reduction procedure aimed at getting rid of nonphysical degrees of freedom. This picture we present is fully covariant and complete: it contains both Lagrangian and Hamiltonian formalisms, in particular the Euler-Lagrange equations. Notice that, the required Geometry of jet bundles is affine (as opposed to the linear Geometry of the tangent bundle). Accordinlgy, the notions of affine duality and affine phase space play a distinguished role in our picture. In particular the Tulczyjew triples in this paper consist of morphisms of double affine-vector bundles which, moreover, preserve suitable presymplectic structures.

Katarzyna Grabowska; Luca Vitagliano

2014-06-25

54

NASA Astrophysics Data System (ADS)

The spectrum of superstring theory on the AdS 5 × S 5 Ramond-Ramond background in tensionless limit contains integer and half-integer higher-spin fields subject at most to two-rows Young tableaux Y( s 1, s 2). We review the details of a gauge-invariant Lagrangian description of such massive and massless higher-spin fields in anti-de-Sitter spaces with arbitrary dimensions. The procedure is based on the construction of Verma modules, its oscillator realizations and of a BFV-BRST operator for non-linear algebras encoding unitary irreducible representations of AdS group.

Reshetnyak, A. A.

2010-11-01

55

The Lagrangian and Hamiltonian functions describing average motion of a relativistic particle under the action of intensive high-frequency electromagnetic radiation are obtained. In weak, low-frequency background fields, such a particle on average drifts with an effective, relativistically invariant mass, which depends on the intensity of the electromagnetic field.

I.Y. Dodin; N.J. Fisch; G.M. Fraiman

2003-02-06

56

NASA Astrophysics Data System (ADS)

The prescription of Silva to derive superpotential equations from variational derivatives rather than from Lagrangian densities is applied to theories of gravity derived from Lovelock Lagrangians in the Palatini representation. Spacetimes are without torsion and isolated sources of gravity are minimally coupled. On a closed boundary of spacetime, the metric is given and the connection coefficients are those of Christoffel. We derive equations for the superpotentials in these conditions. The equations are easily integrated and we give the general expression for all superpotentials associated with Lovelock Lagrangians. We find, in particular, that in Einstein's theory, in any number of dimensions, the superpotential, valid at spatial and at null infinity, is that of Katz, Bi?ák and Lynden-Bell, the KBL superpotential. We also give explicitly the superpotential for Gauss Bonnet theories of gravity. Finally, we find a simple expression for the superpotential of Einstein Gauss Bonnet theories with an anti-de Sitter background: it is minus the KBL superpotential, confirming, as it should, the calculation of the total mass energy of spacetime at spatial infinity by Deser and Tekin.

Katz, Joseph; Livshits, Gideon I.

2008-09-01

57

Metric-like Lagrangian Formulations for Higher-Spin Fields of Mixed Symmetry

We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting extending the metric formulation of linearized gravity, and then the ($\\gamma$-)trace constraints on fields and gauge parameters are eliminated via the introduction of auxiliary fields. We also display the emergence of Weyl-like symmetries in particular classes of models in low space-time dimensions.

Andrea Campoleoni

2009-10-16

58

(Non-)decoupled supersymmetric field theories

NASA Astrophysics Data System (ADS)

We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M . We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism [1-3], we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed = 4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS 4 Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB).

Di Pietro, Lorenzo; Dine, Michael; Komargodski, Zohar

2014-04-01

59

The nonlinear perturbation theory of gravitational instability is extended to include effects of both biasing and redshift-space distortions, which are inevitable in predicting observable quantities in galaxy surveys. Weakly nonlinear effects in galaxy clustering on large scales recently attracted great interest, since the precise determination of scales of baryon acoustic oscillations is crucial to investigate the nature of dark energy by galaxy surveys. We find that a local Lagrangian bias and redshift-space distortions are naturally incorporated in our formalism of perturbation theory with a resummation technique via the Lagrangian picture. Our formalism is applicable to any biasing scheme which is local in Lagrangian space, including the halo bias as a special case. Weakly nonlinear effects on halo clustering in redshift space are analytically given. We assume only a fundamental idea of the halo model: haloes form according to the extended Press-Schechter theory, and the spatial distributions are locally biased in Lagrangian space. There is no need for assuming the spherical collapse model to follow the dynamical evolution, which is additionally assumed in standard halo prescriptions. One-loop corrections to the power spectrum and correlation function of haloes in redshift space are explicitly derived and presented. Instead of relying on expensive numerical simulations, our approach provides an analytic way of investigating the weakly nonlinear effects, simultaneously including the nonlinear biasing and nonlinear redshift-space distortions. Nonlinearity introduces a weak scale dependence in the halo bias. The scale dependence is a smooth function in Fourier space, and the bias does not critically change the feature of baryon acoustic oscillations in the power spectrum. The same feature in the correlation function is less affected by nonlinear effects of biasing.

Matsubara, Takahiko [Department of Physics, Nagoya University, Chikusa, Nagoya, 464-8602 (Japan)

2008-10-15

60

In the framework of the theory with a fundamental mass in the one-loop approximation, we evaluate the exact Lagrange function of the strong constant magnetic field, replacing the Heisenberg–Euler Lagrangian in the traditional QED. We establish that the derived generalization of the Lagrange function is real for arbitrary values of the magnetic field. In the weak field, the evaluated Lagrangian

V. G. Kadyshevsky; V. N. Rodionov

2003-01-01

61

Euler-Heisenberg Lagrangian to all orders in the magnetic field and the Chiral Magnetic Effect

In high energy heavy ion collisions as well as in astrophysical objects like magnetars extreme magnetic field strengths are reached. Thus, there exists a need to calculate divers QED processes to all orders in the magnetic field. We calculate the vacuum polarization graph in second order of the electric field and all orders of the magnetic field resulting in a generalization of the Euler-Heisenberg Lagrangian. We perform the calculation in the effective Lagrangian approach of J. Schwinger as well as using modified Feynman rules. We find that both approaches give the same results provided that the different finite renormalization terms are taken into account. Our results imply that any quantitative explanation of the recently proposed Chiral Magnetic Effect has to take 'Strong QED' effects into account, because these corrections are huge.

Simon Wolfgang Mages; Matthias Aicher; Andreas Schäfer

2010-09-08

62

Euler-Heisenberg Lagrangian to all orders in the magnetic field and the Chiral Magnetic Effect

In high energy heavy ion collisions as well as in astrophysical objects like magnetars extreme magnetic field strengths are reached. Thus, there exists a need to calculate divers QED processes to all orders in the magnetic field. We calculate the vacuum polarization graph in second order of the electric field and all orders of the magnetic field resulting in a generalization of the Euler-Heisenberg Lagrangian. We perform the calculation in the effective Lagrangian approach of J. Schwinger as well as using modified Feynman rules. We find that both approaches give the same results provided that the different finite renormalization terms are taken into account. Our results imply that any quantitative explanation of the recently proposed Chiral Magnetic Effect has to take 'Strong QED' effects into account, because these corrections are huge.

Mages, Simon Wolfgang; Schäfer, Andreas

2010-01-01

63

Information channel capacity in the field theory estimation

NASA Astrophysics Data System (ADS)

The construction of the information capacity for the vector position parameter in the Minkowskian space-time is presented. This lays the statistical foundations of the kinematical term of the Lagrangian of the physical action for many field theory models, derived by the extremal physical information method of Frieden and Soffer.

S?adkowski, J.; Syska, J.

2012-12-01

64

NASA Astrophysics Data System (ADS)

We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on right-movers. The local symmetries include one copy of the Virasoro algebra and a U(1) current algebra. This differs from the two-dimensional conformal group but in some respects is equally powerful in constraining the theory. In particular, the symmetries on a torus lead to modular covariance of the partition function, which is used to derive a universal formula for the asymptotic density of states. For an application we turn to the holographic description of black holes in quantum gravity, motivated by the fact that the symmetries in the near-horizon geometry of any extremal black hole are identical to those of a two-dimensional field theory with chiral scaling. We consider two examples: black holes in warped AdS3 in topologically massive gravity and in string theory. In both cases, the density of states in the two-dimensional field theory reproduces the Bekenstein-Hawking entropy of black holes in the gravity theory.

Detournay, Stéphane; Hartman, Thomas; Hofman, Diego M.

2012-12-01

65

Algebraic Quantum Field Theory

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by S. Doplicher, R. Haag, and J. E. Roberts (DHR); and we give an alternative proof of Doplicher and Roberts' reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix.

Hans Halvorson; Michael Mueger

2006-02-14

66

Effective field theory of cosmological perturbations

NASA Astrophysics Data System (ADS)

The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.

Piazza, Federico; Vernizzi, Filippo

2013-11-01

67

In defence of naivete: The conceptual status of Lagrangian QFT

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the "naive" quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work.

David Wallace

2001-12-23

68

We prove the existence of the Bogoliubov S(g) operator for the (: ?4 :)2 quantum field theory for coupling functions g of compact support in space and time. The construction is nonperturbative and relies on a theorem of Kisynski. It implies almost automatically the properties of unitarity and causality for disjoint supports in the time variable.

Walter F. Wreszinski; Luiz A. Manzoni; Oscar Bolinaa

69

A numerical technique for predicting wind fields using a Lagrangian approach

Lagrangian accelerations in ter~s of the fields of velocity snd geopotcntiel height of s constant pressure surface. The first is based on the simplified equations of horizontal, frictionless motion o. a particle; the second is based on a vsristional... this approximation in describing the actual motion, we are neglecting the smell egeostrophic components of the wind which msy be important in the development of atmospheric systems, Before numerical methods became practical as a forecasting tool, ob]ective wind...

Barnes, Stanley Louis

2012-06-07

70

Lagrangian simulation of a thin non-premixed flame in the field of an asymmetric layer

Development of an analytical, subgrid-scale non-premixed combustion model for simulation of two-dimensional reacting shear flow at conditions of fast chemistry is described. The model is based on generalization of the classical one-dimensional flamelet representation to multi-dimensional flow conditions. and incorporation of resulting combustion model into adaptive, Lagrangian vortex element techniques. Evolution of the external flow field is computed by tracking

Ahmed F. Ghoniem

1996-01-01

71

Nonlinear quantum equations: Classical field theory

NASA Astrophysics Data System (ADS)

An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q ? 1. The main characteristic of this field theory consists on the fact that besides the usual ? (x,t), a new field ? (x,t) needs to be introduced in the Lagrangian, as well. The field ? (x,t), which is defined by means of an additional equation, becomes ? ^{*}(x,t) only when q ? 1. The solutions for the fields ? (x,t) and ? (x,t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E2 = p2c2 + m2c4, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.

Rego-Monteiro, M. A.; Nobre, F. D.

2013-10-01

72

NASA Astrophysics Data System (ADS)

The nuclear field theory (NFT) is presented here with particular emphasis on its foundations. The following points are discussed: i) the equivalence between pure fermion and NFT operators (including the Hamiltonian), ii) the results from an exactly soluble example, iii) the appropriate expansion parameter and the convergence of the corresponding perturbation series and iv) the extension to deformed systems. This is accomplished through the derivation of both the deformed Hamiltonian (superfluid case) and of the perturbational treatment appropriate for deformed basis.

Bes, D. R.

73

NASA Astrophysics Data System (ADS)

The Minimal Multiscale Lagrangian Mapping procedure developed in the context of neutral fluid turbulence is a simple method for generating synthetic vector fields. Using a sequence of low-pass filtered fields, fluid particles are displaced at their rms speed for some scale-dependent time interval, and then interpolated back to a regular grid. Fields produced in this way are seen to possess certain properties of real turbulence. This paper extends the technique to plasmas by taking into account the coupling between the velocity and magnetic fields. We examine several possible applications to plasma systems. One use is as initial conditions for simulations, wherein these synthetic fields may efficiently produce a strongly intermittent cascade. The intermittency properties of the synthetic fields are also compared with those of the solar wind. Finally, studies of cosmic ray transport and modulation in the test particle approximation may benefit from improved realism in synthetic fields produced in this way.

Subedi, P.; Chhiber, R.; Tessein, J. A.; Wan, M.; Matthaeus, W. H.

2014-12-01

74

Reverse engineering quantum field theory

NASA Astrophysics Data System (ADS)

An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.

Oeckl, Robert

2012-12-01

75

Strings and Unified Field Theory

It is argued that string theory predicts unified field theory rather than general relativity coupled to matter fields. In unified field theory all the objects are geometrical, for strings the Kalb-Ramond matter field is identical to the asymmetric part of the metric except that the fields contribute to different sides of the field equations. The dilaton is related to the object of non-metricity.

Mark D. Roberts

2006-07-18

76

NASA Astrophysics Data System (ADS)

On the smallest scales, three-dimensional large-scale structure surveys contain a wealth of cosmological information which cannot be trivially extracted due to the non-linear dynamical evolution of the density field. Lagrangian perturbation theory (LPT) is widely applied to the generation of mock halo catalogs and data analysis. In this work, we compare topological features of the cosmic web such as voids, sheets, filaments and clusters, in the density fields predicted by LPT and full numerical simulation of gravitational large-scale structure formation. We propose a method designed to improve the correspondence between these density fields, in the mildly non-linear regime. We develop a computationally fast and flexible tool for a variety of cosmological applications. Our method is based on a remapping of the approximately-evolved density field, using information extracted from N-body simulations. The remapping procedure consists of replacing the one-point distribution of the density contrast by one which better accounts for the full gravitational dynamics. As a result, we obtain a physically more pertinent density field on a point-by-point basis, while also improving higher-order statistics predicted by LPT. We quantify the approximation error in the power spectrum and in the bispectrum as a function of scale and redshift. Our remapping procedure improves one-, two- and three-point statistics at scales down to 8 Mpc/h.

Leclercq, Florent; Jasche, Jens; Gil-Marín, Héctor; Wandelt, Benjamin

2013-11-01

77

On Lagrangian approach to self-dual gauge fields in spacetime of nontrivial topology

We study the Lagrangian description of chiral bosons, p-form gauge fields with (anti-)self-dual gauge field strengths, in D=2p+2 dimensional spacetime of nontrivial topology. We show that the manifestly Lorentz and diffeomorphism invariant Pasti-Sorokin-Tonin (PST) approach is consistent and produces the (anti-)self-duality equation also in topologically nontrivial spacetime. We discuss in what circumstances the nontrivial topology makes difference between two disconnected, `da-timelike' and `da-spacelike' branches of the PST system, the gauge fixed version of which are described by not manifestly invariant Henneaux-Teitelboim (HT) and Perry-Schwarz (PS) actions, respectively.

Igor Bandos

2014-06-19

78

On Lagrangian approach to self-dual gauge fields in spacetime of nontrivial topology

NASA Astrophysics Data System (ADS)

We study the Lagrangian description of chiral bosons, p-form gauge fields with (anti-)self-dual gauge field strengths, in D = 2 p + 2 dimensional spacetime of non-trivial topology. We show that the manifestly Lorentz and diffeomorphism invariant Pasti-Sorokin-Tonin (PST) approach is consistent and produces the (anti-)self-duality equation also in topologically nontrivial spacetime. We discuss in what circumstances the nontrivial topology makes difference between two disconnected, da-timelike and da-spacelike branches of the PST system, the gauge fixed version of which are described by not manifestly invariant Henneaux-Teitelboim (HT) and Perry-Schwarz (PS) actions, respectively.

Bandos, Igor

2014-08-01

79

Towards a double field theory on para-Hermitian manifolds

In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kähler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kähler case, this bracket is equal to the sum of the Courant brackets of the two Lagrangian foliations of the manifold. Then, we define a canonical connection and an action of the field that correspond to similar objects of double field theory. Another section is devoted to the Marsden-Weinstein reduction in double field theory on para-Hermitian manifolds. Finally, we give examples of fields on some well-known para-Hermitian manifolds.

Vaisman, Izu [Department of Mathematics, University of Haifa, Haifa (Israel)] [Department of Mathematics, University of Haifa, Haifa (Israel)

2013-12-15

80

We describe projection operators in the matter sector of Witten's cubic string field theory using modes on the right and left halves of the string. These projection operators represent a step towards an analytic solution of the equations of motion of the full string field theory, and can be used to construct Dp-brane solutions of the string field theory when

David J. Gross; Washington Taylor

2001-01-01

81

Quantum Mechanics with Basic Field Theory

NASA Astrophysics Data System (ADS)

Preface; 1. Basic formalism; 2. Fundamental commutator and time evolution of state vectors and operators; 3. Dynamical equations; 4. Free particles; 5. Particles with spin 1/2; 6. Gauge invariance, angular momentum and spin; 7. Stern-Gerlach experiments; 8. Some exactly solvable bound state problems; 9. Harmonic oscillator; 10. Coherent states; 11. Two-dimensional isotropic harmonic oscillator; 12. Landau levels and quantum Hall effect; 13. Two-level problems; 14. Spin 1/2 systems in the presence of magnetic field; 15. Oscillation and regeneration in neutrino and neutral K-mesons as two-level systems; 16. Time-independent perturbation for bound states; 17. Time-dependent perturbation; 18. Interaction of charged particles and radiation in perturbation theory; 19. Scattering in one dimension; 20. Scattering in three dimensions - a formal theory; 21. Partial wave amplitudes and phase shifts; 22. Analytic structure of the S-matrix; 23. Poles of the Green's function and composite systems; 24. Approximation methods for bound states and scattering; 25. Lagrangian method and Feynman path integrals; 26. Rotations and angular momentum; 27. Symmetry in quantum mechanics and symmetry groups; 28. Addition of angular momenta; 29. Irreducible tensors and Wigner-Eckart theorem; 30. Entangled states; 31. Special theory of relativity: Klein Gordon and Maxwell's equation; 32. Klein Gordon and Maxwell's equation; 33. Dirac equation; 34. Dirac equation in the presence of spherically symmetric potentials; 35. Dirac equation in a relativistically invariant form; 36. Interaction of Dirac particle with electromagnetic field; 37. Multiparticle systems and second quantization; 38. Interactions of electrons and phonons in condensed matter; 39. Superconductivity; 40. Bose Einstein condensation and superfluidity; 41. Lagrangian formulation of classical fields; 42. Spontaneous symmetry breaking; 43. Basic quantum electrodynamics and Feynman diagrams; 44. Radiative corrections; 45. Anomalous magnetic moment and Lamb shift; Appendix; References; Index.

Desai, Bipin R.

2009-12-01

82

Application of chiral resonance Lagrangian theories to the muon g-2

We think that phenomenological resonance Lagrangian models, constrained by global fits from low energy hadron reaction data, can help to improve muon g-2 predictions. The main issue are those contributions which cannot be calculated by perturbative means: the hadronic vacuum polarization (HVP) effects and the hadronic light--by--light (HLbL) scattering contribution. I review recent progress in the evaluation of the HVP contribution within the broken Hidden Local Symmetry (HLS) framework, worked out in collaboration with M. Benayoun, P. David and L. DelBuono. Our HLS driven estimate reads a_mu (LO had)=(688.60+\\-4.24) 10^{-10} and we find a_mu (theory)= (11 659 177.65 +/- 5.76) 10^{-10}.

Fred Jegerlehner

2013-12-13

83

Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids

A finite volume cell-centered Lagrangian scheme for solving large deformation problems is constructed based on the hypo-elastic model and using the mimetic theory. Rigorous analysis in the context of gas and solid dynamics, and arbitrary polygonal meshes, is presented to demonstrate the ability of cell-centered schemes in mimicking the continuum properties and principles at the discrete level. A new mimetic formulation based gradient evaluation technique and physics-based, frame independent and symmetry preserving slope limiters are proposed. Furthermore, a physically consistent dissipation model is employed which is both robust and inexpensive to implement. The cell-centered scheme along with these additional new features are applied to solve solids undergoing elasto-plastic deformation.

Sambasivan, Shiv Kumar [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory; Burton, Donald E. [Los Alamos National Laboratory; Christon, Mark A. [Los Alamos National Laboratory

2012-07-19

84

We present a method for reconstructing cosmological densityn for and velocity fields using the Lagrangian Zel'dovich formalism. . The method involves finding the least action solution for straight line particle paths in an evolving density field. Our starting point is the final, evolved density , so that we are in effect carrying out the standard Zel'dovich Approximation based process in reverse. Using a simple numerical algorithm we are able to minimise the action for the trajectories of several million particles. We apply our method to the evolved density taken from N-body simulations of different cold dark matter dominated universes, testing both the prediction for the present day velocity field and for the initial density field. The method is easy to apply, reproduces the accuracy of the forward Zel'dovich Approximation, and also works directly in redshift space with minimal modification.

R. A. C. Croft; E. Gaztanaga

1996-02-19

85

Geometrical structures of higher-order dynamical systems and field theories

In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian function/density, or a Hamiltonian that admits Lagrangian counterpart. These geometric frameworks are used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems in field theory.

Pedro D. Prieto-Martínez

2014-10-28

86

In The Quantum Theory of Fields, Nobel Laureate Steven Weinberg combines his exceptional physical insight with his gift for clear exposition to provide a self-contained, comprehensive, and up-to-date introduction to quantum field theory. This is a two-volume work. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by

Steven Weinberg

1995-01-01

87

Nonlinear quantum equations: Classical field theory

An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q? 1. The main characteristic of this field theory consists on the fact that besides the usual ?(x(vector sign),t), a new field ?(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field ?(x(vector sign),t), which is defined by means of an additional equation, becomes ?{sup *}(x(vector sign),t) only when q? 1. The solutions for the fields ?(x(vector sign),t) and ?(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.

Rego-Monteiro, M. A.; Nobre, F. D. [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)] [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)

2013-10-15

88

Generalized gauge field theories with non-topological soliton solutions

We perform a systematic analysis of the conditions under which \\textit{generalized} gauge field theories of compact semisimple Lie groups exhibit electrostatic spherically symmetric non-topological soliton solutions in three space dimensions. By the term \\textit{generalized}, we mean that the dynamics of the concerned fields is governed by lagrangian densities which are general functions of the quadratic field invariants, leading to physically consistent models. The analysis defines exhaustively the class of this kind of lagrangian models supporting those soliton solutions and leads to methods for their explicit determination. The necessary and sufficient conditions for the linear stability of the finite-energy solutions against charge-preserving perturbations are established, going beyond the usual Derrick-like criteria, which only provides necessary conditions.

Joaquin Diaz-Alonso; Diego Rubiera-Garcia

2007-08-04

89

Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field

We develop a relativistic variational model for a nematic liquid crystal interacting with an electro- magnetic field. The constitutive relation for a general anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss light wave propagation in this moving uniaxial medium, for which the corresponding optical metrics are identified explicitly. A Lagrangian for the coupled system of a nematic liquid crystal and the electromagnetic field is constructed, from which a complete set of equations of motion for the system is derived. The canonical energy-momentum and spin tensors are systematically obtained. We compare our results with those within the non-relativistic models. As an application of our general formalism, we discuss the so-called Abraham-Minkowski controversy on the momentum of light in a medium.

Yuri N. Obukhov; Tomas Ramos; Guillermo F. Rubilar

2012-03-14

90

From euclidean field theory to quantum field theory

In order to construct examples for interacting quantum field theory models,\\u000athe methods of euclidean field theory turned out to be powerful tools since\\u000athey make use of the techniques of classical statistical mechanics.\\u000a Starting from an appropriate set of euclidean n-point functions (Schwinger\\u000adistributions), a Wightman theory can be reconstructed by an application of the\\u000afamous Osterwalder-Schrader reconstruction theorem.

Dirk Schlingemann; Theoretische Physik; Erwin Schrodinger

1998-01-01

91

Modern Classical Electrodynamics and Electromagnetic Radiation - Vacuum Field Theory Aspects

The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and related with them physical aspects. Based on the vacuum field theory no-geometry approach, developed in \\cite{BPT,BPT1}, the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. A problem closely related to the radiation reaction force is analyzed aiming to explain the Wheeler and Feynman reaction radiation mechanism, well known as the absorption radiation theory, and strongly dependent on the Mach type interaction of a charged point particle in an ambient vacuum electromagnetic medium. There are discussed some relationships between this problem and the one derived within the context of the vacuum field theory approach. The R. \\ Feynman's \\textquotedblleft heretical\\textquotedblright\\ approach \\cite{Dy1,Dy2} to deriving the Lorentz force based Maxwell electromagnetic equations is also revisited, its complete legacy is argued both by means of the geometric considerations and its deep relation with the vacuum field theory approach devised before in \\cite{BPT0,BPT1}. \\ Being completely classical, we reanalyze the Feynman's derivation from the classical Lagrangian and Hamiltonian points of view \\ and construct its nontrivial \\ relativistic generalization compatible with the mentioned above vacuum field theory approach.

N. N. Bogolubov; A. K. Prykarpatsky

2012-04-25

92

Quantum Field Theory Frank Wilczeky

Quantum Field Theory Frank Wilczeky Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt achieved and prospective. Possible limitations of quantum eld theory are viewed in the light of its history

Wilczek, Frank

93

D-brane effective field theory from string field theory

Open string field theory is considered as a tool for deriving the effective action for the massless or tachyonic fields living on D-branes. Some simple calculations are performed in open bosonic string field theory which validate this approach. The level truncation method is used to calculate successive approximations to the quartic terms ?4 , (A?A?)2 and [A?,A?]2 for the zero

Washington Taylor

2000-01-01

94

Basics in Conformal Field Theory

NASA Astrophysics Data System (ADS)

The approach for studying Conformal Field Theories is somewhat different from the usual approach for Quantum Field Theories. Because, instead of starting with a classical action for the fields and quantising them via the canonical quantisation or the path integral method, one employs the symmetries of the theory. In the spirit of the so-called boot-strap approach, for CFTs one defines and for certain cases even solves the theory just by exploiting the consequences of the symmetries. Such a procedure is possible in two dimensions because the algebra of infinitesimal conformal transformations in this case is very special: it is infinite dimensional.

Blumenhagen, Ralph; Plauschinn, Erik

95

The logarithmic conformal field theories

We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two- and three- point functions. This calculation is done for the general case of more than one logarithmic field in a block, and more than one set of logarithmic fields. Then we show that one can regard the logarithmic field as a formal derivative of the ordinary field with respect to its conformal weight. This enables one to calculate any n-point function containing the logarithmic field in terms of ordinary n-point functions. At last, we calculate the OPE coefficients of a logarithmic conformal field theory, and show that these can be obtained from the corresponding coefficients of ordinary conformal theory by a simple derivation.

Tabar, M R R; Khorrami, M

1996-01-01

96

On the power counting in effective field theories

NASA Astrophysics Data System (ADS)

We discuss the systematics of power counting in general effective field theories, focusing on those that are nonrenormalizable at leading order. As an illuminating example we consider chiral perturbation theory gauged under the electromagnetic U(1) symmetry. This theory describes the low-energy interactions of the octet of pseudo-Goldstone bosons in QCD with photons and has been discussed extensively in the literature. Peculiarities of the standard approach are pointed out and it is shown how these are resolved within our scheme. The presentation follows closely our recent discussion of power counting for the electroweak chiral Lagrangian. The systematics of the latter is reviewed and shown to be consistent with the concept of chiral dimensions. The results imply that naive dimensional analysis (NDA) is incomplete in general effective field theories, while still reproducing the correct counting in special cases.

Buchalla, Gerhard; Catà, Oscar; Krause, Claudius

2014-04-01

97

The existence of momentum and winding modes of closed string on a torus leads to a natural idea that the field theoretical approach of string theory should involve winding type coordinates as well as the usual space-time ...

Kwak, Seung Ki

2012-01-01

98

The effect of spatial and temporal resolutions and random errors on identification of Lagrangian coherent structures (LCSs) from Eulerian velocity fields is evaluated using two canonical flows: a two-dimensional vortex pair and a vortex ring formed by transient ejection of a jet from a tube. The flow field for the vortex pair case was steady and obtained analytically while the transient vortex ring flow was simulated using computational fluid dynamics. To evaluate resolution and random error effects, the flow fields were degraded by locally smoothing the flow and sampling it on a sparser grid to reduce spatial resolution, adding Gaussian distributed random noise to provide random errors, and/or subsampling the time series of vector fields to reduce the temporal resolution (the latter applying only for the vortex ring case). The degradation methods were meant to emulate distortions and errors introduced in common flow measurement methods such as digital particle image velocimetry. Comparing the LCS corresponding to the vortex boundary (separatrix) obtained from the degraded velocity fields with the true separatrix (obtained analytically for the vortex pair case or from high resolution, noise-free velocity fields for the vortex ring case) showed that noise levels as low as 5%-10% of the vortex velocity can cause the separatrix to significantly deviate from its true location in a random fashion, but the "mean" location still remained close to the true location. Temporal and spatial resolution degradations were found to primarily affect transient portions of the flow with strong spatial gradients. Significant deviations in the location of the separatrix were observed even for spatial resolutions as high as 2% of the jet diameter for the vortex ring case. PMID:20370296

Olcay, Ali B; Pottebaum, Tait S; Krueger, Paul S

2010-03-01

99

Theory of fossil magnetic field

Theory of fossil magnetic field is based on the observations, analytical estimations and numerical simulations of magnetic flux evolution during star formation in the magnetized cores of molecular clouds. Basic goals, main features of the theory and manifestations of MHD effects in young stellar objects are discussed.

Dudorov, Alexander E

2014-01-01

100

We reveal nonmanifest gauge and SO(1,5) Lorentz symmetries in the Lagrangian description of a six-dimensional free chiral field derived from the Bagger-Lambert-Gustavsson model in [P.-M. Ho and Y. Matsuo, J. High Energy Phys. 06 (2008) 105.] and make this formulation covariant with the use of a triplet of auxiliary scalar fields. We consider the coupling of this self-dual construction to gravity and its supersymmetrization. In the case of the nonlinear model of [P.-M. Ho, Y. Imamura, Y. Matsuo, and S. Shiba, J. High Energy Phys. 08 (2008) 014.] we solve the equations of motion of the gauge field, prove that its nonlinear field strength is self-dual and find a gauge-covariant form of the nonlinear action. Issues of the relation of this model to the known formulations of the M5-brane worldvolume theory are discussed.

Pasti, Paolo; Tonin, Mario [Dipartimento di Fisica 'Galileo Galilei', Universita degli Studi di Padova (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via F. Marzolo 8, 35131 Padova (Italy); Samsonov, Igor [Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via F. Marzolo 8, 35131 Padova (Italy); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk (Russian Federation); Sorokin, Dmitri [Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via F. Marzolo 8, 35131 Padova (Italy)

2009-10-15

101

Einstein-aether theory with a Maxwell field: General formalism

NASA Astrophysics Data System (ADS)

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.

Balakin, Alexander B.; Lemos, José P. S.

2014-11-01

102

Families of particles with different masses in PT-symmetric quantum field theory

An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's functions of the quantum field theory converges in different pairs of Stokes' wedges in complex field space, and the solutions are physically viable if the pairs of Stokes' wedges are PT symmetric.

C. M. Bender; S. P. Klevansky

2010-02-17

103

Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory

An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's functions of the quantum field theory converges in different pairs of Stokes' wedges in complex-field space, and the solutions are physically viable if the pairs of Stokes' wedges are PT symmetric.

Bender, Carl M. [Physics Department, Washington University, St. Louis, Missouri 63130 (United States); Klevansky, S. P. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 19, 69120 Heidelberg (Germany)

2010-07-16

104

Historical Lagrangian Dynamics

This paper presents (in its Lagrangian version) a very general "historical" formalism for dynamical systems, including time-dynamics and field theories. It is based on the universal notion of history. Its condensed and universal formulation provides a synthesis and a generalization different approaches of dynamics. It is in our sense closer to its real essence. The formalism is by construction explicitely covariant and does not require the introduction of time, or of a time function in relativistic theories. It considers space-time (in field theories) exactly in the same manner than time in usual dynamics, with the only difference that it has 4 dimensions. Both time and space-time are considered as particular cases of the general notion of an evolution domain. In addition, the formalism encompasses the cases where histories are not functions (e.g., of time or of space-time), but forms. This applies to electromag-netism and to first order general relativity (that we treat explicitely). It has both Lagrangian and Hamiltonian versions. An interesting result is the existence of a covariant generalized symplectic form, which generalizes the usual symplectic or the multisymplectic form, and the symplectic currents. Its conservation on shell provides a genuine symplectic form on the space of solutions.

Marc Lachieze-Rey

2014-11-16

105

Analytic progress in open string field theory

Open string field theory provides an action functional for open string fields, and it is thus a manifestly off-shell formulation of open string theory. The solutions to the equation of motion of open string field theory ...

Kiermaier, Michael Stefan

2009-01-01

106

Geometer energy unified field theory

NASA Astrophysics Data System (ADS)

GEOMETER - ENERGY UNIFIED FIELD THEORY Author: Anacleto Rivera Nivón Co-author: Susana Rivera Cabrera This work is an attempt to find the relationship between the Electromagnetic Field and the Gravitational Field. Despite it is based on the existence of Strings of Energy, it is not the same kind of strings that appears on other theories like Superstring Theory, Branas Theory, M - Theory, or any other related string theories. Here, the Strings are concentrated energy lines that vibrates, and experiences shrinking and elongations, absorbing and yielding on each contraction and expansion all that is found in the Universe: matter and antimatter, waves and energy in all manifestations. In contrast to superstring theory, which strings are on the range of the Length of Planck, these Strings can be on the cosmological size, and can contain many galaxies, or clusters, or groups of galaxies; but also they can reach as small sizes as subatomic levels. Besides, and contrary to what it is stated in some other string theories that need the existence of ten or more dimensions, the present proposal sustains in only four particular dimensions. It has been developed a mathematical support that will try to help to improve the understanding of the phenomena that take place at the Universe.

Rivera, Susana; Rivera, Anacleto

107

The Story of \\cal O: Positivity constraints in effective field theories

We propose a simple method for identifying operators in effective field theories whose coefficients must be positive by causality. We also attempt to clarify the relationship between diverse positivity arguments that have appeared in the literature. We conjecture that the superluminal perturbations identified in non-positive effective theories are generally connected to instabilities that develop near the cutoff scale. We discuss implications for the ghost condensate, the chiral Lagrangian, and the Goldstone bosons of theories with spontaneous Lorentz violation.

Alejandro Jenkins; Donal O'Connell

2006-09-22

108

NASA Astrophysics Data System (ADS)

We describe calculations of tunnelling rate constants for the field ion microscope (FIM) using various model potentials, and potentials obtained from self-consistent electronic structure calculations incorporating the full screening of an applied electric field. For our tunnelling calculations we have used the JWKB method of Haydock and Kingham. The expression for the tunnelling rate constant for a flat surface given by Haydock and Kingham is inaccurate and we have derived a new and reliable formula. We have also introduced a new tunnelling potential for the FIM which includes explicitly the effects of image potentials. None of the potentials for smooth surfaces give ionization zone widths which are narrow enough to account for experimental values. However, the width of the ionization zone is found to be a strongly decreasing function of the corrugation of the surface potential, and for large corrugations we can obtain results in plausible agreement with experimental values. For corrugated model surfaces we have found cross-surface variations in the tunnelling rate constant which may be sufficient to account for the atomic resolution of the FIM under normal operating conditions at liquid nitrogen temperatures.

Lam, S. C.; Needs, R. J.

1994-03-01

109

Symmetries, sum rules and constraints on effective field theories

NASA Astrophysics Data System (ADS)

Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the scattering amplitudes in the IR to total cross sections integrated all the way up to the UV. Exploiting the group structure of the symmetry, we systematically determine all the independent sum rules and positivity conditions on the expansion coefficients. For effective field theories the amplitudes in the IR are calculable and hence the sum rules set constraints on the parameters of the effective Lagrangian. We clarify the impact of gauging on the sum rules for Goldstone bosons in spontaneously broken gauge theories. We discuss explicit examples that are relevant for WW-scattering, composite Higgs models, and chiral perturbation theory. Certain sum rules based on custodial symmetry and its extensions provide constraints on the Higgs boson coupling to the electroweak gauge bosons.

Bellazzini, Brando; Martucci, Luca; Torre, Riccardo

2014-09-01

110

Conceptual Foundations of Quantum Field Theory

NASA Astrophysics Data System (ADS)

Introduction: Conceptual issues in quantum field theory; Part I. Philosophers' Interests in Quantum Field Theory: 1. Why are we philosophers interested in quantum field theory; 2. Quantum field theory and the philosopher; Part II. Three Approaches to the Foundations of Quantum Field Theory: 3. The usefulness of a general theory of quantized fields; 4. Effective field theory in condensed matter physics; 5. The triumph and limitations of quantum field theory; 6. Comments; Discussions; Part III. Does Quantum Field Theory Need a Foundation: 7. Does quantum field theory need a foundation?; Part IV. Mathematics, Statistical Mechanics and Quantum Field Theory: 8. Renormalization group theory: its basis and formulation in statistical physics; 9. Where does quantum field theory fit into the big picture?; 10. The unreasonable effectiveness of quantum field theory; 11. Comment: the quantum field theory of physics and of mathematics; Part V. Quantum Field Theory and Spacetime: Introduction; 12. Quantum field theory and spacetime: formalism and reality; 13. Quantum field theory of geometry; 14. 'Localization' in quantum field theory: how much of QFT is compatible with what we know about spacetime; 15. Comments; VI. 16. What is quantum field theory and what did we think it was?; 17. Comments; Discussions; Part VII.Renormalization Group: 18. What is fundamental physics? A renormalization group perspective; 19. Renormalization group: an interesting yet puzzling idea; Part VIII. Non-Abelian Gauge Theory: 20. Gauge fields, gravity and Bohm's theory; 21. Is the Aharonov-Bohm effect local?; Discussions; Part IX. The Ontology of Particles or Fields: 22. The ineliminable classical face of quantum field theory; 23. The logic of quanta; 24. Do Feynman diagrams endorse a particle ontology?; 25. On the ontology of QFT; Part X. Panel Discussion.

Cao, Tian Yu

2004-03-01

111

Magnetic Yang-Mills Theory as an Effective Field Theory of the Gluon Plasma

We propose magnetic SU(N) pure gauge theory as an effective field theory describing the long distance nonperturbative magnetic response of the deconfined phase of Yang-Mills theory. The magnetic non-Abelian Lagrangian, unlike that of electrodynamics where there is exact electromagnetic duality, is not known explicitly, but here we regard the magnetic SU(N) Yang-Mills Lagrangian as the leading term in the long distance effective gauge theory of the plasma phase. In this treatment, which is applicable for a range of temperatures in the interval T_c magnetic energy profile around a spatial Wilson loop in the deconfined phase parallels the formation of an electric flux tube in the confined phase. We use the effective theory to calculate spatial Wilson loops and the magnetic charge density induced in the plasma by the corresponding color electric current loops. These calculations suggest that the deconfined phase of Yang-Mills theory has the properties of a closely-packed fluid of magnetically charged composite objects.

M. Baker

2009-01-20

112

Field theories with « Superconductor » solutions

Summary The conditions for the existence of non-perturbative type « superconductor » solutions of field theories are examined. A non-covariant\\u000a canonical transformation method is used to find such solutions for a theory of a fermion interacting with a pseudoscalar boson.\\u000a A covariant renormalisable method using Feynman integrals is then given. A « superconductor » solution is found whenever in\\u000a the normal

J. Goldstone

1961-01-01

113

Exact scalar field cosmologies in a higher derivative theory

NASA Astrophysics Data System (ADS)

We obtain exact cosmological solutions of a higher derivative theory described by the Lagrangian L = R + 2a R2 in the presence of interacting scalar field. The interacting scalar field potential required for a known evolution of the FRW universe in the framework of the theory is obtained using a technique different from the usual approach to solve the Einstein field equations. We follow here a technique to determine potential similar to that used by Ellis and Madsen in Einstein gravity. Some new and interesting potentials are noted in the presence of R2 term in the Einstein action for the known behaviours of the universe. These potentials in general do not obey the slow rollover approximation.

1999-11-01

114

Generalization of the Darwin Lagrangian

Starting from a Lagrangian treatment of classical electrodynamics and using simple heuristic arguments, an effective generalization of the Darwin Lagrangian for point charges moving with arbitrary velocities (v

Frejlak, W.

1988-06-01

115

NASA Astrophysics Data System (ADS)

Halos are biased tracers of the dark matter distribution. It is often assumed that the initial patches from which halos formed are locally biased with respect to the initial fluctuation field, meaning that the halo-patch fluctuation field can be written as a Taylor series in the dark matter density fluctuation field. If quantities other than the local density influence halo formation, then this Lagrangian bias will generically be nonlocal; the Taylor series must be performed with respect to these other variables as well. We illustrate the effect with Monte Carlo simulations of a model in which halo formation depends on the local shear (the quadrupole of perturbation theory) and provide an analytic model that provides a good description of our results. Our model, which extends the excursion set approach to walks in more than one dimension, works both when steps in the walk are uncorrelated, as well as when there are correlations between steps. For walks with correlated steps, our model includes two distinct types of nonlocality: one is due to the fact that the initial density profile around a patch which is destined to form a halo must fall sufficiently steeply around it—this introduces k dependence to even the linear bias factor, but otherwise only affects the monopole of the clustering signal. The other type of nonlocality is due to the surrounding shear field; this affects the quadratic and higher-order bias factors and introduces an angular dependence to the clustering signal. In both cases, our analysis shows that these nonlocal Lagrangian bias terms can be significant, particularly for massive halos; they must be accounted for in, e.g., analyses of higher-order clustering in Lagrangian or Eulerian space. Comparison of our predictions with measurements of the halo bispectrum in simulations is encouraging. Although we illustrate these effects using halos, our analysis and conclusions also apply to the other constituents of the cosmic web—filaments, sheets and voids.

Sheth, Ravi K.; Chan, Kwan Chuen; Scoccimarro, Román

2013-04-01

116

Topics in Effective Field Theories

NASA Astrophysics Data System (ADS)

In recent years. our understanding of the structure of quantum field theories has benefitted greatly from the introduction and development of effective field theory (EFT) techniques. The EFT language allows for a systematic characterization of interactions between degrees of freedom relevant in a given energy range, even when some of these interactions are induced by new physics at a higher energy, whose details may be complicated or unknown. In situations where the higher energy theory is well understood, it is nevertheless very useful to be able to describe the behavior of fields that are of interest in a given energy regime, without making reference to degrees of freedom present at different energy scales. In particular, this allows for a relatively straightforward comparison of the effects on low energy modes of different high energy interactions. We present here two previously published papers, in each of which the EFT concept plays a central role. In Chapter 1, nonperturbative (instanton) contributions to EFT scattering amplitudes are studied. It is found that when the high energy theory requires all fermions (heavy and light) to participate in such tunneling processes, instantons involving only the light fields are naturally absent in the effective theory. This is true even though no explicit mention of the heavy fermions which have been "integrated out" is made in the effective theory description. The resolution of what had been an apparent paradox in the literature is testimony to the generality and consistency of EFT techniques. In Chapter 2. EFT methods are applied to a problem of immediate practical and experimental interest--the possibility of quark compositeness. Top quark substructure, associated with new interactions present at scales above the top quark mass, but unrelated to electroweak physics, is examined with regard to possible effects on experimentally accessible production and decay rates of known particles. It is found that such new physics is indeed consistent with presently available experimental data, so long as only right handed quark fields participate in the new interactions.

Kaplan, Lev

117

Gravitational radiative corrections from effective field theory

In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures 'post-Minkowskian' corrections to the multipole expansion due to nonlinear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from nonrelativistic binaries, including long distance effects up to 3 post-Newtonian (v{sup 6}) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.

Goldberger, Walter D.; Ross, Andreas [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States)

2010-06-15

118

Background independent action for double field theory

Double field theory describes a massless subsector of closed string theory with both momentum and winding excitations. The gauge algebra is governed by the Courant bracket in certain subsectors of this double field theory. ...

Hohm, Olaf

119

take U to be a unitary n Ã? n matrix. Explicitly, U = exp[-igaa T a ] , (3) where the generators antisymmetric 2nÃ?2n matrix, which when exponentiated yields a real orthogonal 2n-dimensional representation of G matrix. Rewrite the Lagrangian in terms of hermitian fields Ai and Bi defined by: j = 1 2 (Aj + i

California at Santa Cruz, University of

120

Introduction to string theory and conformal field theory

A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.

Belavin, A. A., E-mail: belavin@itp.ac.ru; Tarnopolsky, G. M., E-mail: Hetzif@yandex.r [Russian Academy of Sciences, Landau Institute for Theoretical Physics (Russian Federation)

2010-05-15

121

Asymptotic conservation laws in field theory

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the ADM energy in general relativity.

I. M. Anderson; C. G. Torre

1996-08-01

122

Quantum Field Theory in Condensed Matter Physics

NASA Astrophysics Data System (ADS)

Preface; Acknowledgements; Part I. Introduction to Methods: 1. QFT: language and goals; 2. Connection between quantum and classical: path integrals; 3. Definitions of correlation functions: Wick's theorem; 4. Free bosonic field in an external field; 5. Perturbation theory: Feynman diagrams; 6. Calculation methods for diagram series: divergences and their elimination; 7. Renormalization group procedures; 8. O(N)-symmetric vector model below the transition point; 9. Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion; 10. O(3) nonlinear sigma model in the strong coupling limit; Part II. Fermions: 11. Path integral and Wick's theorem for fermions; 12. Interaction electrons: the Fermi liquid; 13. Electrodynamics in metals; 14. Relativistic fermions: aspects of quantum electrodynamics; 15. Aharonov-Bohm effect and transmutation of statistics; Part III. Strongly Fluctuating Spin Systems: Introduction; 16. Schwinger-Wigner quantization procedure: nonlinear sigma models; 17. O(3) nonlinear sigma model in (2+1) dimensions: the phase diagram; 18. Order from disorder; 19. Jordan-Wigner transformations for spin S=1/2 models in D=1, 2, 3; 20. Majorana representation for spin S=1/2 magnets: relationship to Z2 lattice gauge theories; 21. Path integral representations for a doped antiferromagnet; Part IV. Physics in the World of One Spatial Dimension: Introduction; 22. Model of the free bosonic massless scalar field; 23. Relevant and irrelevant fields; 24. Kosterlitz-Thouless transition; 25. Conformal symmetry; 26. Virasoro algebra; 27. Differential equations for the correlation functions; 28. Ising model; 29. One-dimensional spinless fermions: Tomonaga-Luttinger liquid; 30. One-dimensional fermions with spin: spin-charge separation; 31. Kac-Moody algebras: Wess-Zumino-Novikov-Witten model; 32. Wess-Zumino-Novikov-Witten model in the Lagrangian form: non-Abelian bosonization; 33. Semiclassical approach to Wess-Zumino-Novikov-Witten models; 34. Integrable models: dynamical mass generation; 35. A comparative study of dynamical mass generation in one and three dimensions; 36. One-dimensional spin liquids: spin ladder and spin S=1 Heisenberg chain; 37. Kondo chain; 38. Gauge fixing in non-Abelian theories: (1+1)-dimensional quantum chromodynamics; Select bibliography; Index.

Tsvelik, Alexei M.

2007-01-01

123

Quantum Field Theory in Graphene

This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.

I. V. Fialkovsky; D. V. Vassilevich

2011-11-13

124

Computers for Lattice Field Theories

Parallel computers dedicated to lattice field theories are reviewed with emphasis on the three recent projects, the Teraflops project in the US, the CP-PACS project in Japan and the 0.5-Teraflops project in the US. Some new commercial parallel computers are also discussed. Recent development of semiconductor technologies is briefly surveyed in relation to possible approaches toward Teraflops computers.

Y. Iwasaki

1994-01-26

125

Validation of a Lagrangian dust transport model with data from the Fennec/LADUNEX field campaign

NASA Astrophysics Data System (ADS)

Mineral dust aerosol is a key player in the Earth system. Strong winds over the world's major deserts mobilise and subsequently lift mineral dust high into the atmosphere. Due to the harshness and inaccessibility of desert regions, the exact processes of mobilisation and lifting, and layer formation are still unclear. One major unknown in the dust cycle is the dust source or emission strength. Despite better quantification being key for global models, the assessment of impacts on clouds, radiation and biogeochemical cycles, estimates in the literature from global and regional models span a wide range. Here, we validate the state-of-the-art Lagrangian particle dispersion model FLEXPART, which has been made capable of simulating dust mobilisation and settling, with airborne and ground-based mineral aerosol and turbulence measurements from the Fennec/LADUNEX field campaign, which was carried out over the western Sahara during June 2011. For a selected case study we compare in-situ and remote-sensing data from an aircraft and the CALIOP LIDAR observations with FLEXPART dust transport simulations. The reliability of ECMWF analysis data in the vicinity of a convectively-generated dust plume is assessed using a set of model simulations, in which dust emissions are prescribed manually from SEVIRI satellite images. Dust emission associated with deep moist convection has been recently identified as a key problem. Overall, this research underlines the potential of jointly using measurements and observations from many data sources with models to better understand dust emission processes in the Sahara desert, and to limit model uncertainty.

Sodemann, H.; Lai, M.; Knippertz, P.; Bart, M.; Marenco, F.; McQuaid, J. B.; Rosenberg, P.; Ryder, C.

2012-04-01

126

Electromagnetic form factors of the nucleon in effective field theory

We calculate the electromagnetic form factors of the nucleon to third chiral order in manifestly Lorentz-invariant effective field theory. The rho and omega mesons as well as the Delta(1232) resonance are included as explicit dynamical degrees of freedom. To obtain a self-consistent theory with respect to constraints we consider the proper relations among the couplings of the effective Lagrangian. For the purpose of generating a systematic power counting, the extended on-mass-shell renormalization scheme is applied in combination with the small-scale expansion. The results for the electric and magnetic Sachs form factors are analyzed in terms of experimental data and compared to previous findings in the framework of chiral perturbation theory. The pion-mass dependence of the form factors is briefly discussed.

T. Bauer; J. C. Bernauer; S. Scherer

2012-09-18

127

NASA Astrophysics Data System (ADS)

The Lagrangian assimilation algorithm LAVA (LAgrangian Variational Analysis) is customized for coastal areas in the framework of the TOSCA (Tracking Oil Spills & Coastal Awareness network) Project, to improve the response to maritime accidents in the Mediterranean Sea. LAVA assimilates drifters' trajectories in the velocity fields which may come from either coastal radars or numerical models. In the present study, LAVA is applied to the coastal area in front of Toulon (France). Surface currents are available from a WERA radar network (2km spatial resolution, every 20 minutes) and from the GLAZUR model (1/64° spatial resolution, every hour). The cluster of drifters considered is constituted by 7 buoys, transmitting every 15 minutes for a period of 5 days. Three assimilation cases are considered: i) correction of the radar velocity field, ii) correction of the model velocity field and iii) reconstruction of the velocity field from drifters only. It is found that drifters' trajectories compare well with the ones obtained by the radar and the correction to radar velocity field is therefore minimal. Contrarily, observed and numerical trajectories separate rapidly and the correction to the model velocity field is substantial. For the reconstruction from drifters only, the velocity fields obtained are similar to the radar ones, but limited to the neighbor of the drifter paths.

Berta, Maristella; Bellomo, Lucio; Griffa, Annalisa; Gatimu Magaldi, Marcello; Marmain, Julien; Molcard, Anne; Taillandier, Vincent

2013-04-01

128

Large N limit of orbifold field theories

We consider a certain orbifoldization of the N = 4 field theories that leads to N = 2, 1, 0 field theories in four dimensions. These theories were recently analyzed using the string theory perturbation technique. It was found that in the large N limit all correlation functions of the orbifold theories coincide with those of N = 4, modulo

Michael Bershadsky; Andrei Johansen

1998-01-01

129

Bias in the Effective Field Theory of Large Scale Structures

We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local in space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. We describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of $k/k_{\\rm NL}$ and $k/k_{\\rm M}$, where $k$ is the wavenumber of interest, $k_{\\rm NL}$ is the wavenumber associated to the non-linear scale, and $k_{\\rm M}$ is the comoving wavenumber enclosing the mass of a galaxy.

Leonardo Senatore

2014-06-30

130

Diffeomorphisms in group field theories

We study the issue of diffeomorphism symmetry in group field theories (GFT), using the noncommutative metric representation introduced by A. Baratin and D. Oriti [Phys. Rev. Lett. 105, 221302 (2010).]. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties together the vertex translation invariance of discrete gravity, the flatness constraint of canonical quantum gravity, and the topological (coarse-graining) identities for the 6j symbols. We also show how, for the GFT graphs dual to manifolds, the invariance of the Feynman amplitudes encodes the discrete residual action of diffeomorphisms in simplicial gravity path integrals. We extend the results to GFT models for higher-dimensional BF theories and discuss various insights that they provide on the GFT formalism itself.

Baratin, Aristide [Triangle de la Physique, CPHT Ecole Polytechnique, IPhT Saclay, LPT Orsay and Laboratoire de Physique Theorique, CNRS UMR 8627, Universite Paris XI, F-91405 Orsay Cedex (France); Girelli, Florian [School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia); Oriti, Daniele [Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Muehlenberg 1, 14467 Golm (Germany)

2011-05-15

131

Translations in Quantum Field Theory and the Poincaré Gauge Theory of Gravity

In standard quantum field theory, the one-particle states are classified by the unitary representations of the Poincar\\'e group, whereas the causal fields' classification employs the finite-dimensional (non-unitary) representations of the (homogeneous) Lorentz group. We investigate the possibility of constructing fields that transform under the full representation of the Poincar\\'e group. We show that such fields can be consistently constructed, although the Lagrangians that describe them exhibit explicit dependence on the space-time coordinates. The inclusion of gravity within the framework of the Poincar\\'e gauge theory is then discussed. A new feature that occurs is that the translational gauge fields enter the covariant derivative of matter fields. The Poincar\\'e-gauge approach works still well and leads to interesting consequences. The detailed discussion of the Dirac field is presented and the relation to the earlier accounts on Poincar\\'e-spinors is drawn. Another example that is considered is the Poincar\\'e-vector field. The presentation has a partly didactic character and is addressed to all the readers who are interested in the rudiments of quantum field theory and the gauge description of gravity.

Marcin Ka?mierczak

2009-09-29

132

Haag's theorem in noncommutative quantum field theory

Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.

Antipin, K. V. [Moscow State University, Faculty of Physics (Russian Federation)] [Moscow State University, Faculty of Physics (Russian Federation); Mnatsakanova, M. N., E-mail: mnatsak@theory.sinp.msu.ru [Moscow State University, Skobeltsyn Institute of Nuclear Physics (Russian Federation); Vernov, Yu. S. [Russian Academy of Sciences, Institute for Nuclear Research (Russian Federation)] [Russian Academy of Sciences, Institute for Nuclear Research (Russian Federation)

2013-08-15

133

Spin1 resonance contributions to the weak chiral Lagrangian: The vector field formulation

We use the vector formulation to evaluate vector and axial-vector exchange contributions to the O(p4) weak chiral Lagrangian. We recover in this framework the bulk of the contributions found previously by Ecker et al. in the antisymmetric formulation of vectors and axial-vectors, but new interesting features arise: (i) most of our results are independent of Factorization and (ii) novel contributions

Giancarlo D'Ambrosio; Jorge Portolés

1998-01-01

134

Effective field theory in nuclear physics

I review recent developments in the application of effective field theory to nuclear physics. Emphasis is placed on precision two-body calculations and efforts to formulate the nuclear shell model in terms of an effective field theory.

Martin J. Savage

2000-12-12

135

Effective Field Theory in Nuclear Physics

I review recent developments in the application of effective field theory to nuclear physics. Emphasis is placed on precision two-body calculations and efforts to formulate the nuclear shell model in terms of an effective field theory.

Martin J. Savage

2000-07-11

136

Motion of small bodies in classical field theory

I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.

Gralla, Samuel E. [Enrico Fermi Institute and Department of Physics University of Chicago 5640 S. Ellis Avenue, Chicago, Illinois 60637 (United States)

2010-04-15

137

Particle decay in Ising field theory with magnetic field

The scaling limit of the two-dimensional Ising model in the plane of temperature and magnetic field defines a field theory which provides the simplest illustration of non-trivial phenomena such as spontaneous symmetry breaking and confinement. Here we discuss how Ising field theory also gives the simplest model for particle decay. The decay widths computed in this theory provide the obvious test ground for the numerical methods designed to study unstable particles in quantum field theories discretized on a lattice.

Gesualdo Delfino

2007-03-30

138

Quantum Field Theory in (0 + 1) Dimensions

ERIC Educational Resources Information Center

We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…

Boozer, A. D.

2007-01-01

139

Controllability and Motion Algorithms for Underactuated Lagrangian Systems on Lie Groups

Controllability and Motion Algorithms for Underactuated Lagrangian Systems on Lie Groups Francesco on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater vehicle in terms of the symmet- ric product and the Lie bracket of the input vector fields. Perturbation theory

Bullo, Francesco

140

A Lagrangian particle model has been adapted to examine human exposures to particulate matter < or = 10 microm (PM10) in agricultural settings. This paper reports the performance of the model in comparison to extensive measurements by elastic LIDAR (light detection and ranging). For the first time, the LIDAR measurements allowed spatially distributed and time dynamic measurements to be used to test the predictions of a field-scale model. The model outputs, which are three-dimensional concentration distribution maps from an agricultural disking operation, were compared with the LIDAR-scanned images. The peak cross-correlation coefficient and the offset distance of the measured and simulated plumes were used to quantify both the intensity and location accuracy. The appropriate time averaging and changes in accuracy with height of the plume were examined. Inputs of friction velocity, Monin-Obukhov length, and wind direction (1 sec) were measured with a three-axis sonic anemometer at a single point in the field (at 1.5-m height). The Lagrangian model of Wang et al. predicted the near-field concentrations of dust plumes emitted from a field disking operation with an overall accuracy of approximately 0.67 at 3-m height. Its average offset distance when compared with LIDAR measurements was approximately 38 m, which was 6% of the average plume moving distance during the simulation periods. The model is driven by weather measurements, and its near-field accuracy is highest when input time averages approach the turbulent flow time scale (3-70 sec). The model accuracy decreases with height because of smoothing and errors in the input wind field, which is modeled rather than measured at heights greater than the measurement anemometer. The wind steadiness parameter (S) can be used to quantify the combined effects of wind speed and direction on model accuracy. PMID:19947118

Wang, Junming; Hiscox, April L; Miller, David R; Meyer, Thomas H; Sammis, Ted W

2009-11-01

141

Permutation Orbifolds in Conformal Field Theories and String Theory

We summarize the results obtained in the last few years about permutation orbifolds in two-dimensional conformal field theories, their application to string theory and their use in the construction of four-dimensional heterotic string models.

M. Maio

2011-11-03

142

Einstein's vierbein field theory of curved space

General Relativity theory is reviewed following the vierbein field theory approach proposed in 1928 by Einstein. It is based on the vierbein field taken as the "square root" of the metric tensor field. Einstein's vierbein theory is a gauge field theory for gravity; the vierbein field playing the role of a gauge field but not exactly like the vector potential field does in Yang-Mills theory--the correction to the derivative (the covariant derivative) is not proportional to the vierbein field as it would be if gravity were strictly a Yang-Mills theory. Einstein discovered the spin connection in terms of the vierbein fields to take the place of the conventional affine connection. To date, one of the most important applications of the vierbein representation is for the derivation of the correction to a 4-spinor quantum field transported in curved space, yielding the correct form of the covariant derivative. Thus, the vierbein field theory is the most natural way to represent a relativistic quantum field theory in curved space. Using the vierbein field theory, presented is a derivation of the the Einstein equation and then the Dirac equation in curved space. Einstein's original 1928 manuscripts translated into English are included.

Jeffrey Yepez

2011-06-10

143

Large N field theories, string theory and gravity

We review the holographic correspondence between field theories and string\\/M theory, focusing on the relation between compactifications of string\\/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime

Ofer Aharony; Steven S. Gubser; Juan Maldacena; Hirosi Ooguri; Yaron Oz

2000-01-01

144

Nuclear field theory of Fermi systems in an external field

Nuclear field theory (NFT) is developed for interacting Fermi systems in an external field by using path integral techniques. The NFT representation of the external field operator together with the corresponding diagrammatic rules are strictly derived.

H. Reinhardt

1978-01-01

145

An introduction to topological field theories

Topological field theories may be roughly defined as those for which the correlation functions for observables are precisely topological invariants. The study of such theories is interesting from the mathematical point of view, since they give one the possibility for finding new topological invariants within the framework of field theory. They are also physically interesting due to the interpretation of

J. Roca; Departament d'Estructura

1993-01-01

146

Quantum Field Theory in Condensed Matter Physics

This course in modern quantum field theory for condensed matter physics includes a derivation of the path integral representation, Feynman diagrams and elements of the theory of metals. Alexei Tsvelik also covers Landau Fermi liquid theory and gradually turns to more advanced methods used in the theory of strongly correlated systems. The book contains a thorough exposition of such non-perturbative

Alexei M. Tsvelik

2003-01-01

147

Holographic dual of free field theory

We derive a holographic dual description of free quantum field theory in arbitrary dimensions, by reinterpreting the exact renormalization group to obtain a higher spin gravity theory of the general type which had been proposed and studied as a dual theory. We show that the dual theory reproduces all correlation functions.

Douglas, Michael R.; Mazzucato, Luca; Razamat, Shlomo S. [Simons Center for Geometry and Physics and YITP, Stony Brook University, Stony Brook, New York 11794 (United States)

2011-04-01

148

We generalize QCD at asymptotically large isospin chemical potential to an arbitrary even number of flavors. We also allow for small quark chemical potentials, which stress the coincident Fermi surfaces of the paired quarks and lead to a sign problem in Monte Carlo simulations. We derive the corresponding low-energy effective theory in both $p$- and $\\epsilon$-expansion and quantify the severity of the sign problem. We construct the random matrix theory describing our physical situation and show that it can be mapped to a known random matrix theory at low baryon density so that new insights can be gained without additional calculations. In particular, we explain the Silver Blaze phenomenon at high isospin density. We also introduce stressed singular values of the Dirac operator and relate them to the pionic condensate. Finally we comment on extensions of our work to two-color QCD.

Takuya Kanazawa; Tilo Wettig

2014-06-24

149

Noncommutative Tachyons And String Field Theory

It has been shown recently that by turning on a large noncommutativity parameter, the description of tachyon condensation in string theory can be drastically simplified. We reconsider these issues from the standpoint of string field theory, showing that, from this point of view, the key fact is that in the limit of a large B-field, the string field algebra factors

Edward Witten

2000-01-01

150

Classical and quantum conformal field theory

We define chiral vertex operators and duality matrices and review the fundamental identities they satisfy. In order to understand the meaning of these equations, and therefore of conformal field theory, we define the classical limit of a conformal field theory as a limit in which the conformal weights of all primary fields vanish. The classical limit of the equations for

Gregory Moore; Nathan Seiberg

1989-01-01

151

Einstein's vierbein field theory of curved space

General Relativity theory is reviewed following the vierbein field theory approach proposed in 1928 by Einstein. It is based on the vierbein field taken as the "square root" of the metric tensor field. Einstein's vierbein theory is a gauge field theory for gravity; the vierbein field playing the role of a gauge field but not exactly like the vector potential field does in Yang-Mills theory--the correction to the derivative (the covariant derivative) is not proportional to the vierbein field as it would be if gravity were strictly a Yang-Mills theory. Einstein discovered the spin connection in terms of the vierbein fields to take the place of the conventional affine connection. To date, one of the most important applications of the vierbein representation is for the derivation of the correction to a 4-spinor quantum field transported in curved space, yielding the correct form of the covariant derivative. Thus, the vierbein field theory is the most natural way to represent a relativistic quantum field theory in...

Yepez, Jeffrey

2011-01-01

152

Heating Field Theory the ``Environmentally Friendly'' Way!

We discuss how to implement an ``environmentally friendly'' renormalization in the context of finite temperature field theory. Environmentally friendly renormalization provides a method for interpolating between the different effective field theories which characterize different asymptotic regimes. We give explicit two loop Pad\\'e resummed results for $\\l\\ff$ theory for $T>T_c$. We examine the implications for non-Abelian gauge theories.

M. A. van Ejick; Denjoe O'Connor; C. R. Stephens

1993-10-31

153

Heating Field Theory the ``Environmentally Friendly'' Way!

We discuss how to implement an ``environmentally friendly'' renormalization in the context of finite temperature field theory. Environmentally friendly renormalization provides a method for interpolating between the different effective field theories which characterize different asymptotic regimes. We give explicit two loop Pad\\'e resummed results for $\\l\\ff$ theory for $T>T_c$. We examine the implications for non-Abelian gauge theories.

Van Eijck, M A; Stephens, C R; Connor, Denjoe O'

1993-01-01

154

Effective field theory calculation of second post-Newtonian binary dynamics

We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second post-Newtonian order equations of motion in harmonic gauge in a straightforward manner.

Gilmore, James B.; Ross, Andreas [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States)

2008-12-15

155

The quantum character of physical fields. Foundations of field theories

The existing field theories are based on the properties of closed exterior forms, which are invariant ones and correspond to conservation laws for physical fields. Hence, to understand the foundations of field theories and their unity, one has to know how such closed exterior forms are obtained. In the present paper it is shown that closed exterior forms corresponding to field theories are obtained from the equations modelling conservation (balance)laws for material media. It has been developed the evolutionary method that enables one to describe the process of obtaining closed exterior forms. The process of obtaining closed exterior forms discloses the mechanism of evolutionary processes in material media and shows that material media generate, discretely, the physical structures, from which the physical fields are formed. This justifies the quantum character of field theories. On the other hand, this process demonstrates the connection between field theories and the equations for material media and points to the fact that the foundations of field theories must be conditioned by the properties of material media. It is shown that the external and internal symmetries of field theories are conditioned by the degrees of freedom of material media. The classification parameter of physical fields and interactions, that is, the parameter of the unified field theory, is connected with the number of noncommutative balance conservation laws for material media.

L. I. Petrova

2006-03-15

156

Boundary conditions in quantum field theories

A question worth addressing in theories of the nucleus derived from field theories is the determination of the parameters which enter into the theory. If a parameters is dimensionless, as is the nucleon-nucleon pi meson strong interaction coupling constant, it is conceivable that is can be determined using field theory. The coupling constant might then be determined by a condition placed on the functions which describe the solution. In this work it is shown that such a solution cannot exist. Several interesting and important quantum field theories must contain the coupling constant in the boundary conditions. The theories considered in the present discussion include quantum electrodynamics of spin-1/2 fermions and gauge field theories. 5 refs.

Burt, P.B. (Clemson Univ., SC (United States))

1993-06-01

157

Unified Field Theories Hitoshi Murayama

review of two successful theories which unified two apparently distinct forces: Maxwell's theory of electromagnetism and GlashowÂSalamÂWeinberg theory of electroweak forces. Then it describes known four forces in Nature: gravitational, electromagnetic, weak and strong forces, and what their similarities

Murayama, Hitoshi

158

Functional Integration for Quantum Field Theory

The functional integration scheme for path integrals advanced by Cartier and DeWitt-Morette is extended to the case of fields. The extended scheme is then applied to quantum field theory. Several aspects of the construction are discussed.

J. LaChapelle

2006-10-16

159

Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories

With the covariant formulation in hand from the first paper of this series (physics/9801019), we begin in this second paper to study the canonical (or ``instantaneous'') formulation of classical field theories. The canonical formluation works with fields defined as time-evolving cross sections of bundles over a Cauchy surface, rather than as sections of bundles over spacetime as in the covariant formulation. In Chapter 5 we begin to relate these approaches to classical field theory; in particular, we show how covariant multisymplectic geometry induces the instantaneous symplectic geometry of cotangent bundles of sections of fields over a Cauchy surface. In Chapter 6, we proceed to consider field dynamics. A crucial feature of our discussion here is the degeneracy of the Lagrangian functionals for the field theories of interest. As a consequence of this degeneracy, we have constraints on the choice of initial data, and gauge freedom in the evolution of the fields. Chapter 6 considers the role of initial value constraints and gauge transformations in Hamiltonian field dynamics. In Chapter 7, we then describe how covariant momentum maps defined on the multiphase space induce "energy-momentum maps'' on the instantaneous phase spaces. We show that for a group action which leaves the Cauchy surface invariant, this energy-momentum map coincides with the usual notion of a momentum map. We also show, when the gauge group"includes'' the spacetime diffeomorphism group, that one of the components of the energy-momentum map corresponding to spacetime diffeomorphisms can be identified (up to sign) with the Hamiltonian for the theory.

Mark J. Gotay; James Isenberg; Jerrold E. Marsden

2004-11-09

160

The spinor field theory of the photon

I introduce a spinor field theory for the photon. The three-dimensional vector electromagnetic field and the four-dimensional vector potential are components of this spinor photon field. A spinor equation for the photon field is derived from Maxwell's equations,the relations between the electromagnetic field and the four-dimensional vector potential, and the Lorentz gauge condition. The covariant quantization of free photon field is done, and only transverse photons are obtained. The vacuum energy divergence does not occur in this theory. A covariant "positive frequency" condition is introduced for separating the photon field from its complex conjugate in the presence of the electric current and charge.

Ruo Peng Wang

2011-09-15

161

We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux $Y(s_1,...,s_k)$ with $k\\geq 2$ rows on $d$-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for $k=2$ Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic $sp(2k)$ algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin $(s_1,s_2)$ is derived.

Burdik, Cestmir

2011-01-01

162

We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux $Y(s_1,...,s_k)$ with $k\\geq 2$ rows on $d$-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for $k=2$ Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic $sp(2k)$ algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin $(s_1,s_2)$ is derived.

Cestmir Burdik; Alexander Reshetnyak

2011-11-23

163

NASA Astrophysics Data System (ADS)

We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux Y(s1,..., sk) with ? >= 2 rows on d-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for ? = 2 Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic sp(2?) algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin (s1, s2) is derived.

Burdík, ?.; Reshetnyak, A.

2012-02-01

164

We construct a ultraviolet completion of the bosonic sector of 11-dimensional supergravity motivated by string field theory. We start from a general class of theories characterized by an entire nonpolynomial form factor which allows one to avoid new poles in the propagator and improves the high-energy behavior of the loops amplitudes. Comparing these models with effective string field theory, a unique form factor is selected out. In view of this, we modify 10-dimensional supergravity and finally get a ultraviolet completion of 11-dimensional supergravity by an oxidation process. The result is a candidate for a finite and unitary particle-field limit of M-theory.

Gianluca Calcagni; Leonardo Modesto

2014-04-08

165

Classical field theory. Advanced mathematical formulation

In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of this classical field theory by means of ghosts and antifields for the purpose of its quantization.

G. Sardanashvily

2008-11-03

166

The Global Approach to Quantum Field Theory

Thanks to its impressive success in the second half of the 20th century, both in high-energy physics and in critical phenomena, quantum field theory has enjoyed an abundant literature. We therefore greet yet another book on this subject with caution: what can a monograph on quantum field theory bring now that is new, either conceptually or pedagogically? But when it

Antoine Folacci; Bruce Jensen

2003-01-01

167

String Field Theory Around the Tachyon Vacuum

Assuming that around the tachyon vacuum the kinetic term of cubic open string field theory is made purely of ghost operators we are led to gauge invariant actions which manifestly implement the absence of open string dynamics around this vacuum. We test this proposal by showing the existence of lump solutions of arbitrary codimension in this string field theory. The

Leonardo Rastelli; Ashoke Sen; Barton Zwiebach

2000-01-01

168

Effective Field Theory for Top Quark Physics

Physics beyond the standard model can affect top-quark physics indirectly. We describe the effective field theory approach to describing such physics, and contrast it with the vertex-function approach that has been pursued previously. We argue that the effective field theory approach has many fundamental advantages and is also simpler.

Cen Zhang; Scott Willenbrock

2010-08-18

169

Quantum Cellular Automata from Lattice Field Theories

We apply the methods of lattice field theories to the quantization of cellular automata. We discuss the quantization of five main categories of cellular automata: bosonic, fermionic, supersymmetric, spin and quantum dot using path integral and operator formalisms of lattice field theories. We show that the quantization of supersymmetric cellular automata is related to recently discussed string bit models of

Michael McGuigan

2003-01-01

170

Numerical Object Oriented Quantum Field Theory Calculations

The qft++ package is a library of C++ classes that facilitate numerical (not algebraic) quantum field theory calculations. Mathematical objects such as matrices, tensors, Dirac spinors, polarization and orbital angular momentum tensors, etc. are represented as C++ objects in qft++. The package permits construction of code which closely resembles quantum field theory expressions, allowing for quick and reliable calculations.

M. Williams

2008-05-19

171

Quantum Statistical Field Theory and Combinatorics

This is a set of review notes on combinatorial aspects of Bosonic quantum field theory. We collect together several related issues concerning moments of distributions, moments of stochastic processes and Ito's formula, and Green's functions and cumulant moments in quantum field theory.

John Gough

2003-11-24

172

Lectures on Topological Quantum Field Theory

What follows are lecture notes about Topological Quantum Field Theory. While the lectures were aimed at physicists, the content is highly mathematical in its style and motivation. The subject of Topological Quantum Field Theory is young and developing rapidly in many directions. These lectures are not at all representative of this activity, but rather reflect particular interests of the author.

Daniel S. Freed

1992-01-01

173

NASA Astrophysics Data System (ADS)

We introduce a tool to determine surface fluxes from atmospheric concentration data in the midst of distributed sources or sinks over land, the Stochastic Time-Inverted Lagrangian Transport (STILT) model, and illustrate the use of the tool with CO2 data over North America. Anthropogenic and biogenic emissions of trace gases at the surface cause large variations of atmospheric concentrations in the planetary boundary layer (PBL) from the "near field," where upstream sources and sinks have strong influence on observations. Transport in the near field often takes place on scales not resolved by typical grid sizes in transport models. STILT provides the capability to represent near-field influences, transforming this noise to signal useful in diagnosing surface emissions. The model simulates transport by following the time evolution of a particle ensemble, interpolating meteorological fields to the subgrid scale location of each particle. Turbulent motions are represented by a Markov chain process. Significant computational savings are realized because the influence of upstream emissions at different times is modeled using a single particle simulation backward in time, starting at the receptor and sampling only the portion of the domain that influences the observations. We assess in detail the physical and numerical requirements of STILT and other particle models necessary to avoid inconsistencies and to preserve time symmetry (reversibility). We show that source regions derived from backward and forward time simulations in STILT are similar, and we show that deviations may be attributed to violation of mass conservation in currently available analyzed meterological fields. Using concepts from information theory, we show that the particle approach can provide significant gains in information compared to conventional gridcell models, principally during the first hours of transport backward in time, when PBL observations are strongly affected by surface sources and sinks.

Lin, J. C.; Gerbig, C.; Wofsy, S. C.; Andrews, A. E.; Daube, B. C.; Davis, K. J.; Grainger, C. A.

2003-08-01

174

A canonical structure for classical field theories

A general scheme of constructing a canonical structure (i.e. Poisson bracket, canonical fields) in classical field theories is proposed. The theory is manifestly independent of the particular choice of an initial space-like surface in space-time. The connection between dynamics and canonical structure is established. Applications to theories with a gauge and constraints are of special interest. Several physical examples are

Jerzy Kijowski; Wiktor Szczyrba

1976-01-01

175

Computer Stochastics in Scalar Quantum Field Theory

This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point properties and logarithmic corrections, partition function zeroes, the triviality bound on the Higgs mass, finite size effects, Goldstone bosons and chiral perturbation theory, and the determination of scattering phase shifts for some scalar models.

C. B. Lang

1993-12-01

176

Descent relations in cubic superstring field theory

NASA Astrophysics Data System (ADS)

The descent relations between string field theory (SFT) vertices are characteristic relations of the operator formulation of SFT and they provide self-consistency of this theory. The descent relations langleV2|V1rangle and langleV3|V1rangle in the NS fermionic string field theory in the ? and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.

Aref'eva, I. Y.; Gorbachev, R.; Medvedev, P. B.; Rychkov, D. V.

2008-01-01

177

Conformal Field Theory Correlators from Classical Scalar Field Theory on $AdS_{d+1}$

We use the correspondence between scalar field theory on $AdS_{d+1}$ and a\\u000aconformal field theory on $R^d$ to calculate the 3- and 4-point functions of\\u000athe latter. The classical scalar field theory action is evaluated at tree\\u000alevel.

W. Muck; K. S. Viswanathan

1998-01-01

178

Pilot-wave theory and quantum fields

Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector, but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilot-wave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilot-wave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schroedinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilot-wave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.

Ward Struyve

2007-07-25

179

Space–time noncommutative field theories and unitarity

We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space–time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there

Jaume Gomis; Thomas Mehen

2000-01-01

180

Relativistic theory of infinite statistics fields

Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. However, the validity of relativistic quon theories is still in doubt. In this paper we prove that there exists a relativistic quantum field theory which allows interactions involving infinite statistics particles. We also give some consistency analysis of this theory, such as conservation of statistics and Feynman rules.

Cao Chao; Chen Yixin; Li Jianlong [Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027 (China)

2009-12-15

181

Scattering theory for dipole quantum fields

In the present work a general frame for the scattering theory of local, relativistic dipole quantum fields is presented and some models of interacting dipole fields are considered, i.e. local, relativistic quantum fields with indefinite metric which asymptotically do not converge to free fields, but to free dipole fields. Also, we give explicit formulae for the (nontrivial) scattering matrix of dipole in- and out- fields for these models. Furthermore we show how related dipole degrees of freedom occur in the perturbation theory of certain two dimensional models, e.g. massive sine-Gordon or sinh-Gordon models.

H. Gottschalk

2007-03-10

182

Green functions in stochastic field theory

NASA Astrophysics Data System (ADS)

Functional representations are reviewed for the generating function of Green functions of stochastic problems stated either with the use of the Fokker-Planck equation or the master equation. Both cases are treated in a unified manner based on the operator approach similar to quantum mechanics. Solution of a second-order stochastic differential equation in the framework of stochastic field theory is constructed. Ambiguities in the mathematical formulation of stochastic field theory are discussed. The Schwinger-Keldysh representation is constructed for the Green functions of the stochastic field theory which yields a functional-integral representation with local action but without the explicit functional Jacobi determinant or ghost fields.

Honkonen, Juha

2013-03-01

183

Giant Gravitons in Conformal Field Theory

Giant gravitons in AdS5 × S5, and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three

Vijay Balasubramanian; Micha Berkooz; Asad Naqvi; Matthew J. Strassler

2002-01-01

184

Atomic Probes of Noncommutative Field Theory

We consider the role of Lorentz symmetry in noncommutative field theory. We find that a Lorentz-violating standard-model extension involving ordinary fields is general enough to include any realisitc noncommutative field theory as a subset. This leads to various theoretical consequences, as well as bounds from existing experiments at the level of (10 TeV)$^{-2}$ on the scale of the noncommutativity parameter.

Charles D. Lane

2002-01-07

185

It is shown that the classical field equations pertaining to gravity coupled to other bosonic fields are equivalent to a single geodesic equation, describing the free fall of a point particle in superspace. Some implications for quantum gravity are discussed.

J. Greensite

1995-08-14

186

Path integral quantization of parametrised field theory

Free scalar field theory on a flat spacetime can be cast into a generally covariant form known as parametrised field theory in which the action is a functional of the scalar field as well as the embedding variables which describe arbitrary, in general curved, foliations of the flat spacetime. We construct the path integral quantization of parametrised field theory in order to analyse issues at the interface of quantum field theory and general covariance in a path integral context. We show that the measure in the Lorentzian path integral is non-trivial and is the analog of the Fradkin- Vilkovisky measure for quantum gravity. We construct Euclidean functional integrals in the generally covariant setting of parametrised field theory using key ideas of Schleich and show that our constructions imply the existence of non-standard `Wick rotations' of the standard free scalar field 2 point function. We develop a framework to study the problem of time through computations of scalar field 2 point functions. We illustrate our ideas through explicit computation for a time independent 1+1 dimensional foliation. Although the problem of time seems to be absent in this simple example, the general case is still open. We discuss our results in the contexts of the path integral formulation of quantum gravity and the canonical quantization of parametrised field theory.

Madhavan Varadarajan

2004-04-06

187

The facets of relativistic quantum field theory

NASA Astrophysics Data System (ADS)

Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.

Dosch, H. G.; Müller, V. F.

2010-04-01

188

The facets of relativistic quantum field theory

NASA Astrophysics Data System (ADS)

Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.

Dosch, H. G.; Müller, V. F.

2011-04-01

189

Introduction to conformal field theory and string theory

These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs.

Dixon, L.J.

1989-12-01

190

Computational Methods in Quantum Field Theory

After a brief introduction to the statistical description of data, these lecture notes focus on quantum field theories as they emerge from lattice models in the critical limit. For the simulation of these lattice models, Markov chain Monte-Carlo methods are widely used. We discuss the heat bath and, more modern, cluster algorithms. The Ising model is used as a concrete illustration of important concepts such as correspondence between a theory of branes and quantum field theory or the duality map between strong and weak couplings. The notes then discuss the inclusion of gauge symmetries in lattice models and, in particular, the continuum limit in which quantum Yang-Mills theories arise.

Kurt Langfeld

2007-11-19

191

Mass corrections in string theory and lattice field theory

Kaluza-Klein (KK) compactifications of higher-dimensional Yang-Mills theories contain a number of 4-dimensional scalars corresponding to the internal components of the gauge field. While at tree level the scalar zero modes are massless, it is well known that quantum corrections make them massive. We compute these radiative corrections at 1 loop in an effective field theory framework, using the background field method and proper Schwinger-time regularization. In order to clarify the proper treatment of the sum over KK modes in the effective field theory approach, we consider the same problem in two different UV completions of Yang-Mills: string theory and lattice field theory. In both cases, when the compactification radius R is much bigger than the scale of the UV completion (R>>{radical}({alpha}{sup '}), a), we recover a mass renormalization that is independent of the UV scale and agrees with the one derived in the effective field theory approach. These results support the idea that the value of the mass corrections is, in this regime, universal for any UV completion that respects locality and gauge invariance. The string analysis suggests that this property holds also at higher loops. The lattice analysis suggests that the mass of the adjoint scalars appearing in N=2, 4 super Yang-Mills is highly suppressed, even if the lattice regularization breaks all supersymmetries explicitly. This is due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.

Del Debbio, Luigi; Kerrane, Eoin; Russo, Rodolfo [SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); Centre for Research in String Theory, Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom)

2009-07-15

192

Three approaches to classical thermal field theory

Research Highlights: > Classical thermal field theory admits three equivalent path integral formulations. > Classical Feynman rules can be derived for all three formulations. > Quantum Feynman rules reduce to classical ones at high temperatures. > Classical Feynman rules become much simpler when superfields are introduced. - Abstract: In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.

Gozzi, E., E-mail: gozzi@ts.infn.it [Department of Physics, University of Trieste, Strada Costiera 11, Miramare - Grignano, 34151 Trieste (Italy); INFN, Sezione di Trieste (Italy); Penco, R., E-mail: rpenco@syr.edu [Department of Physics, Syracuse University, Syracuse, NY 13244-1130 (United States)

2011-04-15

193

Quantum Field Theory and the Standard Model

NASA Astrophysics Data System (ADS)

Part I. Field Theory: 1. Microscopic theory of radiation; 2. Lorentz invariance and second quantization; 3. Classical Field Theory; 4. Old-fashioned perturbation theory; 5. Cross sections and decay rates; 6. The S-matrix and time-ordered products; 7. Feynman rules; Part II. Quantum Electrodynamics: 8. Spin 1 and gauge invariance; 9. Scalar QED; 10. Spinors; 11. Spinor solutions and CPT; 12. Spin and statistics; 13. Quantum electrodynamics; 14. Path integrals; Part III. Renormalization: 15. The Casimir effect; 16. Vacuum polarization; 17. The anomalous magnetic moment; 18. Mass renormalization; 19. Renormalized perturbation theory; 20. Infrared divergences; 21. Renormalizability; 22. Non-renormalizable theories; 23. The renormalization group; 24. Implications of Unitarity; Part IV. The Standard Model: 25. Yang-Mills theory; 26. Quantum Yang-Mills theory; 27. Gluon scattering and the spinor-helicity formalism; 28. Spontaneous symmetry breaking; 29. Weak interactions; 30. Anomalies; 31. Precision tests of the standard model; 32. QCD and the parton model; Part V. Advanced Topics: 33. Effective actions and Schwinger proper time; 34. Background fields; 35. Heavy-quark physics; 36. Jets and effective field theory; Appendices; References; Index.

Schwartz, Matthew D.

2014-03-01

194

221B Lecture Notes Quantum Field Theory III (Radiation Field)

221B Lecture Notes Quantum Field Theory III (Radiation Field) 1 Quantization of Radiation Field Early development of quantum mechanics was led by the fact that electro- magnetic radiation is the convenient choice, while for highly rel- ativistic systems such as in high-energy physics. We use Coulomb

Murayama, Hitoshi

195

221B Lecture Notes Quantum Field Theory IV (Radiation Field)

221B Lecture Notes Quantum Field Theory IV (Radiation Field) 1 Quantization of Radiation Field Early development of quantum mechanics was led by the fact that electro- magnetic radiation is the convenient choice, while for highly rel- ativistic systems such as in high-energy physics. We use Coulomb

Murayama, Hitoshi

196

The Absolute Field Constant in the New Field Theory

IN the modification of Maxwell's theory proposed by one of us1, the notion of an `absolute field', called b, played an essential part. In the electrostatic case, the universal constant b is simply the upper limit of the field strength, whilst in the general case of an arbitrary field, b sets a limit to the possible values of when and

Max Born; Erwin Schrödinger

1935-01-01

197

N=2 gauge theories and degenerate fields of Toda theory

We discuss the correspondence between degenerate fields of the W{sub N} algebra and punctures of Gaiotto's description of the Seiberg-Witten curve of N=2 superconformal gauge theories. Namely, we find that the type of degenerate fields of the W{sub N} algebra, with null states at level one, is classified by Young diagrams with N boxes, and that the singular behavior of the Seiberg-Witten curve near the puncture agrees with that of W{sub N} generators. We also find how to translate mass parameters of the gauge theory to the momenta of the Toda theory.

Kanno, Shoichi; Matsuo, Yutaka; Shiba, Shotaro [Department of Physics, Faculty of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Tachikawa, Yuji [School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540 (United States)

2010-02-15

198

General Embedded Brane Effective Field Theories

We present a new general class of four-dimensional effective field theories with interesting global symmetry groups. These theories arise from purely gravitational actions for (3+1)-dimensional branes embedded in higher dimensional spaces with induced gravity terms. The simplest example is the well known Galileon theory, with its associated Galilean symmetry, arising as the limit of a DGP brane world. However, we demonstrate that this is a special case of a much wider range of theories, with varying structures, but with the same attractive features such as second order equations. In some circumstances, these new effective field theories allow potentials for the scalar fields on curved space, with small masses protected by non-linear symmetries. Such models may prove relevant to the cosmology of both the early and late universe.

Garrett Goon; Kurt Hinterbichler; Mark Trodden

2011-03-30

199

Austerity and Geometric Structure of Field Theories

NASA Astrophysics Data System (ADS)

The relation between the austerity idea and the geometric structure of the three basic field theories- -electrodynamics, Yang-Mills theory, and general relativity --is studied. The idea of austerity was originally suggested by J. A. Wheeler in an attempt to formulate the laws of physics in such a way that they would come into being only within "the gates of time" extending from big bang to big crunch, rather than exist from everlasting to everlasting. One of the most significant manifestations of the austerity idea in field theories is thought to be expressed by the boundary of a boundary principle (BBP). The BBP says that almost all content of the field theories can be deduced from the topological identity (PAR-DIFF)(CCIRC)(PAR -DIFF) = 0 used twice, at the 1-2-3-dimensional level (providing the homgeneous field equations), and at the 2-3-4-dimensional level (providing the conservation laws for the source currents). There are some difficulties in this line of thought due to the apparent lack of universality in application of the BBP to the three basic modern field theories--electrodynamics, Yang-Mills theory, and general relativity. This dissertation: (a) analyses the difficulties by means of algebraic topology, integration theory and modern differential geometry based on the concepts of principal bundles and Ehresmann connections; (b) extends the BBP to the unified Kaluza-Klein theory; (c) reformulates the inhomogeneous field equations and the BBP in terms of E. Cartan moment of rotation, in the way universal for all the three theories and compatible with the original austerity idea; (d) underlines the important role of the soldering structure on spacetime, and indicates that the future development of the austerity idea would involve the generalized theories, including the soldering form as a dynamical variable rather than as a background structure.

Kheyfets, Arkady

200

Double field theory of type II strings

We use double field theory to give a unified description of the low energy limits of type IIA and type IIB superstrings. The Ramond-Ramond potentials fit into spinor representations of the duality group O(D, D) and ...

Hohm, Olaf

201

Effective Field Theory for Nuclear Physics

I summarize the motivation for the effective field theory approach to nuclear physics, and highlight some of its recent accomplishments. The results are compared with those computed in potential models.

David B. Kaplan

1999-01-01

202

Quantum field theories on the Lefschetz thimble

In these proceedings, we summarize the Lefschetz thimble approach to the sign problem of Quantum Field Theories. In particular, we review its motivations, and we summarize the results of the application of two different algorithms to two test models.

M. Cristoforetti; F. Di Renzo; A. Mukherjee; L. Scorzato

2013-12-04

203

Effective Field Theory in Condensed Matter Physics

Some personal reminiscences are followed by a brief illustration of how effective field theories are used in condensed matter physics. Examples include Landau's Fermi liquid, sigma models with topological terms, Dirac fermions and the Gross Neveu model.

R. Shankar

1997-01-01

204

Conformal Field Theories in Fractional Dimensions

NASA Astrophysics Data System (ADS)

We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary conformal field theories connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of ?4 theory in the ? expansion.

El-Showk, Sheer; Paulos, Miguel; Poland, David; Rychkov, Slava; Simmons-Duffin, David; Vichi, Alessandro

2014-04-01

205

A 2D- fractional supersymmetry theory is algebraically constructed. The Lagrangian is derived using an adapted superspace including, in addition to a scalar field, two fields with spins 1/3,2/3. This theory turns out to be a rational conformal field theory. The symmetry of this model goes beyond the super Virasoro algebra and connects these third-integer spin states. Besides the stress-momentum tensor, we obtain a supercurrent of spin 4/3. Cubic relations are involved in order to close the algebra; the basic algebra is no longer a Lie or a super-Lie algebra. The central charge of this model is found to be 5/3. Finally, we analyse the form that a local invariant action should take.

A. Perez; M. Rausch de Traubenberg; P. Simon

1996-03-22

206

A 2D- fractional supersymmetry theory is algebraically constructed. The Lagrangian is derived using an adapted superspace including, in addition to a scalar field, two fields with spins 1/3,2/3. This theory turns out to be a rational conformal field theory. The symmetry of this model goes beyond the super Virasoro algebra and connects these third-integer spin states. Besides the stress-momentum tensor, we obtain a supercurrent of spin 4/3. Cubic relations are involved in order to close the algebra; the basic algebra is no longer a Lie or a super-Lie algebra. The central charge of this model is found to be 4/3. Finally, we analyse the form that a local invariant action should take.

Pérez, A; Simon, P; de Traubenberg, M Rausch

1996-01-01

207

Particle Physics and Introduction to Field Theory

The gamut of modern particle physics is presented. Topics included are a self-contained introduction to standard quantum field theory, a discussion of solitons, a detailed discussion of symmetry principles in particle physics, including symmetry breaking, and the formalism and physical ideas of non-Abelain gauge theories and Quantum Chromodynamics. Recent original research by the author is presented. The book concludes with

T. D. Lee; Sidney Drell

1981-01-01

208

Fractional Statistics in Algebraic Quantum Field Theory

the essential features needed for an analysis within the framework of gauge-theory. Chapter 3 describes a U(1Fractional Statistics in Algebraic Quantum Field Theory and the Fractional Quantum Hall . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Fractional Charged Quasiparticle Excitations . . . . . . . . . . . 19 2.3 Hierarchy of FQHE

van Elburg, Ronald A.J.

209

RATIONAL SYMPLECTIC FIELD THEORY FOR LEGENDRIAN KNOTS

, Symplectic Field Theory (SFT), which was introduced by Eliashberg, Givental, and Hofer about a decade ago [EGH00]. The relevant portion of the SFT package for our purposes is a filtered theory for contact puncture, SFT counts holomorphic curves with arbitrarily many positive punctures. In the "closed" case (in

Ng, Lenny

210

Generating Functional in String Field Theory

In our paper, we introduce a path integral of general functional field in order to build the path integral formalism in string field theory from the fact that a string field is a functional field, and describe a method for calculating it in the case of "Gauss-type". We also obtain the generating functional of an open bosonic string and the corresponding Feynman diagram.

Am-Gil Ri; Tae-Song Kim; Song-Jin Im

2013-11-23

211

Geometric continuum regularization of quantum field theory

An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.

Halpern, M.B. (California Univ., Berkeley, CA (USA). Dept. of Physics)

1989-11-08

212

Branes and supersymmetric quantum field theories

NASA Astrophysics Data System (ADS)

Since the discovery of D-branes as non-perturbative, dynamic objects in string theory, various configurations of branes in type IIA/B string theory and M-theory have been considered to study their low-energy dynamics described by supersymmetric quantum field theories. One example of such a construction is based on the description of Seiberg-Witten curves of four-dimensional N = 2 supersymmetric gauge theories as branes in type IIA string theory and M-theory. This enables us to study the gauge theories in strongly-coupled regimes. Spectral networks are another tool for utilizing branes to study non-perturbative regimes of two- and four-dimensional supersymmetric theories. Using spectral networks of a Seiberg-Witten theory we can find its BPS spectrum, which is protected from quantum corrections by supersymmetry, and also the BPS spectrum of a related two-dimensional N = (2,2) theory whose (twisted) superpotential is determined by the Seiberg-Witten curve. When we don't know the perturbative description of such a theory, its spectrum obtained via spectral networks is a useful piece of information. In this thesis we illustrate these ideas with examples of the use of Seiberg-Witten curves and spectral networks to understand various two- and four-dimensional supersymmetric theories. First, we examine how the geometry of a Seiberg-Witten curve serves as a useful tool for identifying various limits of the parameters of the Seiberg-Witten theory, including Argyres-Seiberg duality and Argyres-Douglas fixed points. Next, we consider the low-energy limit of a two-dimensional N = (2, 2) supersymmetric theory from an M-theory brane configuration whose (twisted) superpotential is determined by the geometry of the branes. We show that, when the two-dimensional theory flows to its infra-red fixed point, particular cases realize Kazama-Suzuki coset models. We also study the BPS spectrum of an Argyres-Douglas type superconformal field theory on the Coulomb branch by using its spectral networks. We provide strong evidence of the equivalence of superconformal field theories from different string-theoretic constructions by comparing their BPS spectra.

Park, Chan Youn

213

EFT naturalness: an effective field theory analysis of Higgs naturalness

We investigate naturalness in the Standard Model (SM) Higgs sector in the presence of new heavy physics with typical scale \\Lambda, below which the SM is assumed to be valid. We use effective field theory (EFT) techniques to determine the conditions under which the 1-loop corrections to m_h from the heavy physics can balance those created by SM loop effects, a condition we denote by "EFT naturalness". We obtain the higher dimensional (n \\ge 5) operators in the effective Lagrangian that can lead to EFT naturalness, and classify the underlying heavy theories that can generate such operators at tree-level. In particular, we show that such heavy physics models must contain one or more singlet or triplet heavy bosons or else a singlet, doublet or triplet fermions. We also discuss the experimental constraints on the effective operators and find that if the scale of new physics is hh (V=W,Z) and \\psi \\psi --> hh (\\psi is a SM quark or lepton), or in h+quark(jet) or h+lepton(\\ell or \

Shaouly Bar-Shalom; Amarjit Soni; Jose Wudka

2014-05-12

214

Dark energy or modified gravity? An effective field theory approach

NASA Astrophysics Data System (ADS)

We take an Effective Field Theory (EFT) approach to unifying existing proposals for the origin of cosmic acceleration and its connection to cosmological observations. Building on earlier work where EFT methods were used with observations to constrain the background evolution, we extend this program to the level of the EFT of the cosmological perturbations — following the example from the EFT of Inflation. Within this framework, we construct the general theory around an assumed background which will typically be chosen to mimic ?CDM, and identify the parameters of interest for constraining dark energy and modified gravity models with observations. We discuss the similarities to the EFT of Inflation, but we also identify a number of subtleties including the relationship between the scalar perturbations and the Goldstone boson of the spontaneously broken time translations. We present formulae that relate the parameters of the fundamental Lagrangian to the speed of sound, anisotropic shear stress, effective Newtonian constant, and Caldwell's varpi parameter, emphasizing the connection to observations. It is anticipated that this framework will be of use in constraining individual models, as well as for placing model-independent constraints on dark energy and modified gravity model building.

Bloomfield, Jolyon; Flanagan, Éanna É.; Park, Minjoon; Watson, Scott

2013-08-01

215

Asymptotic states and renormalization in Lorentz-violating quantum field theory

NASA Astrophysics Data System (ADS)

Asymptotic single-particle states in quantum field theories with small departures from Lorentz symmetry are investigated perturbatively with focus on potential phenomenological ramifications. To this end, one-loop radiative corrections for a sample Lorentz-violating Lagrangian contained in the Standard-Model Extension are studied at linear order in Lorentz breakdown. It is found that the spinor kinetic operator, and thus the free-particle physics, is modified by Lorentz-violating operators absent from the original Lagrangian. As a consequence of this result, both the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism need to be adapted. The necessary adaptations are worked out explicitly at first order in Lorentz-breaking coefficients.

Cambiaso, Mauro; Lehnert, Ralf; Potting, Robertus

2014-09-01

216

Generating functionals and Lagrangian partial differential equations

NASA Astrophysics Data System (ADS)

The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton-Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.

Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin

2013-08-01

217

Generating functionals and Lagrangian partial differential equations

The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.

Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)] [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)

2013-08-15

218

Superstring field theory in the democratic picture

We present a new open superstring field theory, whose string fields carry an arbitrary picture number and reside in the large Hilbert space. The redundancy related to picture number is resolved by treating picture changing as a gauge transformation. A mid-point insertion is imperative for this formalism. We find that this mid-point insertion must include all multi-picture changing operators. It is also proven that this insertion as well as all the multi-picture changing operators are zero weight conformal primaries. This new theory solves the problems with the Ramond sector shared by other RNS string field theories, while naturally unifying the NS and Ramond string fields. When partially gauge fixed, it reduces in the NS sector to the modified cubic superstring field theory. Hence, it shares all the good properties of this theory, e.g., it has analytical vacuum and marginal deformation solutions. Treating the redundant gauge symmetry using the BV formalism is straightforward and results in a cubic action with a single string field, whose quantum numbers are unconstrained. The generalization to an arbitrary brane system is simple and includes the standard Chan-Paton factors and the most general string field consistent with the brane system.

Michael Kroyter

2009-11-16

219

8.324 Relativistic Quantum Field Theory II, Fall 2005

This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth ...

Zwiebach, Barton

220

MEDSLIK-II, a Lagrangian marine oil spill model for short-term forecasting - Part 1: Theory

NASA Astrophysics Data System (ADS)

The processes of transport, diffusion and transformation of surface oil in seawater can be simulated using a Lagrangian model formalism coupled with Eulerian circulation models. This paper describes the formalism and the conceptual assumptions of a Lagrangian marine oil slick numerical model and re-writes the constitutive equations in a modern mathematical framework. The Lagrangian numerical representation of the oil slick requires three different state variables: the slick, the particle and the structural state variables. Transformation processes (evaporation, spreading, dispersion and coastal adhesion) act on the slick state variables, while particles variables are used to model the transport and diffusion processes. The slick and particle variables are recombined together to compute the oil concentration in water, a structural state variable. The mathematical and numerical formulation of oil transport, diffusion and transformation processes described in this paper, together with the many simplifying hypothesis and parameterizations, form the basis of a new, open source Lagrangian surface oil spill model, so-called MEDSLIK-II. Part 2 of this paper describes the applications of MEDSLIK-II to oil spill simulations that allow the validation of the model results and the study of the sensitivity of the simulated oil slick to different model numerical parameterizations.

De Dominicis, M.; Pinardi, N.; Zodiatis, G.

2013-03-01

221

Geodesic Detection of Lagrangian Transport Barriers

NASA Astrophysics Data System (ADS)

Lagrangian transport barriers can be viewed as optimal material skeletons for observed tracer patterns. This idea leads to a variational problem whose solution forms the basis of the recent theory of geodesic transport barriers. This geodesic theory enables the computation of hyperbolic barriers (stable and and unstable manifolds), elliptic barriers (Lagrangian eddy boundaries), and parabolic barriers (Lagrangian jet cores) as parametrized curves in two-dimensional, finite-time velocity data sets. We show applications to numerical and observational geophysical flow data.

Haller, George

2013-04-01

222

Dark matter, Elko fields and Weinberg's quantum field theory formalism

The Elko quantum field was introduced by Ahluwalia and Grumiller, who proposed it as a candidate for dark matter. We study the Elko field in Weinberg's formalism for quantum field theory. We prove that if one takes the symmetry group to be the full Poincar\\'e group then the Elko field is not a quantum field in the sense of Weinberg. This confirms results of Ahluwalia, Lee and Schritt, who showed using a different approach that the Elko field does not transform covariantly under rotations and hence has a preferred axis.

Adam Gillard; Benjamin Martin

2010-12-24

223

Quantum meaning of classical field theory

Recent researches have shown that it is possible to obtain information about the physical content of nontrivial quantum field theories by semiclassical methods. This article reviews some of these investigations. We discuss how solutions to field equations, treated as classical, c-number nonlinear differential equations, expose unexpected states in the quantal Hilbert space with novel quantum numbers which arise from topological

R. Jackiw

1977-01-01

224

D-branes and string field theory

In this thesis we study the D-brane physics in the context of Witten's cubic string field theory. We compute first few terms the low energy effective action for the non-abelian gauge field A, from Witten's action. We show ...

Sigalov, Ilya

2006-01-01

225

Effective metric in nonlinear scalar field theories

We discuss several features of the propagation of perturbations in nonlinear scalar field theories using the effective metric. It is shown that the effective metric can be classified according to whether the gradient of the scalar field is timelike, null, or spacelike, and this classification is illustrated with two examples. We shall also show that different signatures for the effective metric are allowed.

E. Goulart; Santiago Esteban Perez Bergliaffa

2011-08-16

226

Nonperturbative Quantum Field Theory in Astrophysics

The extreme electromagnetic or gravitational fields associated with some astrophysical objects can give rise to macroscopic effects arising from the physics of the quantum vacuum. Therefore, these objects are incredible laboratories for exploring the physics of quantum field theories. In this dissertation, we explore this idea in three astrophysical scenarios.

Dan Mazur

2012-09-20

227

Field-theory approach for strings

An approach to string theory is developed on the basis of a covariant effective action for fields corresponding to the excitation modes of the string. Both closed and open bosonic strings are considered. A low-energy approximation to the effective action is derived and the structure of the interactions of the dilation field is established.

Tsei-brevetlin

1986-01-01

228

Phase-space quantization of field theory.

In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.

Curtright, T.; Zachos, C.

1999-04-20

229

Generalized metric formulation of double field theory

The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple formulation with manifest T-duality of the double field theory that describes the massless sector of closed strings. The gauge transformations are written in terms of a generalized Lie derivative whose commutator algebra is defined by a double field theory extension of the Courant bracket.

Olaf Hohm; Chris Hull; Barton Zwiebach

2010-06-24

230

Ecological Field Theory: the concept and field tests

Ecological field theory (EFT) quantifies plant spatial influences as pulsating geometric zones about individual plants. It provides the basis for a methodology to include spatial interactions between plants of different size, function and growth-form in models of plant community dynamics. The key components of EFT are: 1. the influence domain of individuals (D), 2. the field intensity within the domains

J. Walker; P. J. H. Sharpe; L. K. Penridge; H. Wu

1989-01-01

231

Quantum Cellular Automata from Lattice Field Theories

We apply the methods of lattice field theories to the quantization of cellular automata. We discuss the quantization of five main categories of cellular automata: bosonic, fermionic, supersymmetric, spin and quantum dot using path integral and operator formalisms of lattice field theories. We show that the quantization of supersymmetric cellular automata is related to recently discussed string bit models of Thorn and Bergman and represents a link of cellular automata theory to fundamental physics. We discuss spin and quantum dot cellular automata for their importance in experimental realizations and their use in quantum computation. Previous studies of quantum cellular automata utilize the wave function values as cell contents and the discretized linear Dirac equation as an update equation. We show that our approach to the quantization of fermionic cellular automata includes this utilization as a field equation, and in addition allows for nonlinearity through lattice field interactions.

Michael McGuigan

2003-07-24

232

Topics in Supersymmetric Quantum Field Theory

NASA Astrophysics Data System (ADS)

This thesis describes several new tools for analyzing supersymmetric quantum field theories, focusing on theories with four supercharges in three and four dimensions. In chapter two, we discuss supercurrents, supersymmetry multiplets that include the energy-momentum tensor. Physically, different supercurrents give rise to different brane charges in the supersymmetry algebra. They also encode different ways of placing supersymmetric field theories on a curved manifold. Under certain conditions this procedure preserves some of the supersymmetry. In chapter three, we explore these conditions for the case of four-dimensional N = 1 theories with a U(1)R symmetry. In particular, we find that a manifold admits a single supercharge if and only if it is Hermitian. In chapter four, we shift the focus to three-dimensional field theories. We study Chern-Simons contact terms -- contact terms of conserved currents and the energy-momentum tensor, which are associated with Chern-Simons terms for background fields. While the integer parts of these contact terms are ambiguous, their fractional parts constitute new meaningful observables. In N = 2 supersymmetric theories with a U(1) R symmetry certain Chern-Simons contact terms can lead to a novel superconformal anomaly. In chapter five, we use this understanding to elucidate the structure of the free energy F of these theories on a three sphere. In particular, we prove the F-maximization principle for N = 2 superconformal theories. We also explain why computing F via localization leads to a complex answer, even though we expect it to be real in unitary theories.

Dumitrescu, Thomas

233

Lattice Field Theory Methods in Modern Biophysics

An effective field theory exists describing a very large class of biophysically interesting Coulomb gas systems: the lowest order (mean-field) version of this theory takes the form of a generalized Poisson-Boltzmann theory. Interaction terms depend on details (finite-size effects, multipole properties, etc). Convergence of the loop expansion holds only if mutual interactions of mobile charges are small compared to their interaction with the fixed-charge environment, which is frequently not the case. Problems with the strongly- coupled effective theory can be circumvented with an alternative local lattice formulation, with real positive action. In realistic situations, with variable dielectric, a determinant of the Poisson operator must be inserted to generate correct electrostatics. Methods adopted from unquenched lattice QCD do this very efficiently.

Anthony Duncan

2006-09-28

234

Quantum field theory based on birefringent modified Maxwell theory

NASA Astrophysics Data System (ADS)

In the current paper the properties of a birefringent Lorentz-violating extension of quantum electrodynamics is considered. The theory results from coupling modified Maxwell theory, which is a CPT-even Lorentz-violating extension of the photon sector, to a Dirac theory of standard spin-1/2 particles. It is then restricted to a special birefringent case with one nonzero Lorentz-violating coefficient. The modified dispersion laws of electromagnetic waves are obtained plus their phase and group velocities are considered. After deriving the photon propagator and the polarization vectors for a special momentum configuration we prove both unitarity at tree level and microcausality for the quantum field theory based on this Lorentz-violating modification. These analytical proofs are done for a spatial momentum with two vanishing components and the proof of unitarity is supported by numerical investigations in case all components are nonvanishing. The upshot is that the theory is well behaved within the framework of our assumptions where there is a possible issue for negative Lorentz-violating coefficients. The paper shall provide a basis for the future analysis of alternative birefringent quantum field theories.

Schreck, M.

2014-04-01

235

Quantum field theory based on birefringent modified Maxwell theory

In the current paper the properties of a birefringent Lorentz-violating extension of quantum electrodynamics is considered. The theory results from coupling modified Maxwell theory, which is a CPT-even Lorentz-violating extension of the photon sector, to a Dirac theory of standard spin-1/2 particles. It is then restricted to a special birefringent case with one nonzero Lorentz-violating coefficient. The modified dispersion laws of electromagnetic waves are obtained plus their phase and group velocities are considered. After deriving the photon propagator and the polarization vectors for a special momentum configuration we prove both unitarity at tree-level and microcausality for the quantum field theory based on this Lorentz-violating modification. These analytical proofs are done for a spatial momentum with two vanishing components and the proof of unitarity is supported by numerical investigations in case all components are nonvanishing. The upshot is that the theory is well-behaved within the framework of our assumptions where there is a possible issue for negative Lorentz-violating coefficients. The paper shall provide a basis for the future analysis of alternative birefringent quantum field theories.

M. Schreck

2013-10-31

236

Effective Field Theory Beyond the Standard Model

NASA Astrophysics Data System (ADS)

We review the effective field theory approach to physics beyond the Standard Model using dimension-six operators. Topics include the choice of operator basis, electroweak boson pair production, precision electroweak physics (including one-loop contributions), and Higgs physics. By measuring the coefficients of dimension-six operators with good accuracy, we can hope to infer some or all of the features of the theory that lies beyond the Standard Model.

Willenbrock, Scott; Zhang, Cen

2014-10-01

237

Tachyon condensation in string field theory

It has been conjectured that at a stationary point of the tachyon potential for the D-brane of bosonic string theory, the negative energy density exactly cancels the D-brane tension. We evaluate this tachyon potential by off-shell calculations in open string field theory. Surprisingly, the condensation of the tachyon mode alone into the stationary point of its cubic potential is found

Ashoke Sen; Barton Zwiebach

2000-01-01

238

Non Perturbative Aspects of Field Theory

For any quantum field theory (QFT), there exists a set of Schwinger-Dyson equations (SDE) for all its Green functions. However, it is not always straight forward to extract quantitatively exact physical information from this set of equations, especially in the non perturbative regime. The situation becomes increasingly complex with growing number of external legs. I give a qualitative account of the hunt for the non perturbative Green functions in gauge theories.

Bashir, A. [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Apartado Postal 2-82, Morelia, Michoacn 58040 (Mexico)

2009-04-20

239

a Nonassociative Quaternion Scalar Field Theory

NASA Astrophysics Data System (ADS)

A nonassociative Groenewold-Moyal (GM) plane is constructed using quaternion-valued function algebras. The symmetrized multiparticle states, the scalar product, the annihilation/creation algebra and the formulation in terms of a Hopf algebra are also developed. Nonassociative quantum algebras in terms of position and momentum operators are given as the simplest examples of a framework whose applications may involve string theory and nonlinear quantum field theory.

Giardino, Sergio; Teotônio-Sobrinho, Paulo

2013-11-01

240

Tachyon condensation in superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the D-brane–anti-D-brane pair or for the non-BPS D-brane of superstring theories, the negative energy density cancels the brane tensions. We study this conjecture using a Wess–Zumino–Witten-like open superstring field theory free of contact term divergences and recently shown to give 60% of the vacuum energy by

Nathan Berkovits; Ashoke Sen; Barton Zwiebach

2000-01-01

241

Multisymplectic effective General Boundary Field Theory

The transfer matrix in lattice field theory connects the covariant and the initial data frameworks; in spin foam models, it can be written as a composition of elementary cellular amplitudes/propagators. We present a framework for discrete spacetime classical field theory in which solutions to the field equations over elementary spacetime cells may be amalgamated if they satisfy simple gluing conditions matching the composition rules of cellular amplitudes in spin foam models. Furthermore, the formalism is endowed with a multisymplectic structure responsible for local conservation laws. Some models within our framework are effective theories modeling a system at a given scale. Our framework allows us to study coarse graining and the continuum limit.

Mona Arjang; José A. Zapata

2013-12-11

242

Multisymplectic effective general boundary field theory

NASA Astrophysics Data System (ADS)

The transfer matrix in lattice field theory connects the covariant and the initial data frameworks; in spin foam models, it can be written as a composition of elementary cellular amplitudes/propagators. We present a framework for discrete spacetime classical field theory in which solutions to the field equations over elementary spacetime cells may be amalgamated if they satisfy simple gluing conditions matching the composition rules of cellular amplitudes in spin foam models. Furthermore, the formalism is endowed with a multisymplectic structure responsible for local conservation laws. Some models within our framework are effective theories modeling a system at a given scale. Our framework allows us to study coarse graining and the continuum limit.

Arjang, Mona; Zapata, José A.

2014-05-01

243

Experimental Bounds on Classical Random Field Theories

Alternative theories to quantum mechanics motivate important fundamental tests of our understanding and descriptions of the smallest physical systems. Here, using spontaneous parametric downconversion as a heralded single-photon source, we place experimental limits on a class of alternative theories, consisting of classical field theories which result in power-dependent normalized correlation functions. In addition, we compare our results with standard quantum mechanical interpretations of our spontaneous parametric downconversion source over an order of magnitude in intensity. Our data match the quantum mechanical expectations, and do not show a statistically significant dependence on power, limiting on quantum mechanics alternatives which require power-dependent autocorrelation functions.

Joffrey K. Peters; Jingyun Fan; Alan L. Migdall; Sergey V. Polyakov

2014-11-18

244

Diagrammar in classical scalar field theory

In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.

Cattaruzza, E., E-mail: Enrico.Cattaruzza@gmail.com [Department of Physics (Miramare Campus), University of Trieste, Strada Costiera 11, Miramare-Grignano 34014, Trieste (Italy); Gozzi, E., E-mail: gozzi@ts.infn.it [Department of Physics (Miramare Campus), University of Trieste, Strada Costiera 11, Miramare-Grignano 34014, Trieste (Italy); INFN, Sezione di Trieste (Italy); Francisco Neto, A., E-mail: antfrannet@gmail.com [Departamento de Engenharia de Producao, Administracao e Economia, Escola de Minas, Campus Morro do Cruzeiro, UFOP, 35400-000 Ouro Preto MG (Brazil)

2011-09-15

245

Non-exponential decay in Quantum Mechanics and Quantum Field Theory

NASA Astrophysics Data System (ADS)

We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.

Giacosa, Francesco

2014-10-01

246

Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators

We present a complete list of the independent dimension-7 operators that are constructed using the Standard Model degrees of freedom and are invariant under the Standard Model gauge group. This list contains only 20 independent operators; far fewer than the 63 operators available at dimension 6. All of these dimension-7 operators contain fermions and violate lepton number, and 7 of the 20 violate baryon number as well. This result extends the Standard Model Effective Field Theory (SMEFT) and allows a more detailed exploration of the structure and properties of possible deformations from the Standard Model Lagrangian.

Landon Lehman

2014-10-15

247

Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators

We present a complete list of the independent dimension-7 operators that are constructed using the Standard Model degrees of freedom and are invariant under the Standard Model gauge group. This list contains only 20 independent operators; far fewer than the 63 operators available at dimension 6. All of these dimension-7 operators contain fermions and violate lepton number, and 7 of the 20 violate baryon number as well. This result extends the Standard Model Effective Field Theory (SMEFT) and allows a more detailed exploration of the structure and properties of possible deformations from the Standard Model Lagrangian.

Lehman, Landon

2014-01-01

248

Scalar Quantum Field Theory in Disordered Media

A free massive scalar field in inhomogeneous random media is investigated. The coefficients of the Klein-Gordon equation are taken to be random functions of the spatial coordinates. The case of an annealed-like disordered medium, modeled by centered stationary and Gaussian processes, is analyzed. After performing the averages over the random functions, we obtain the two-point causal Green's function of the model up to one-loop. The disordered scalar quantum field theory becomes qualitatively similar to a $\\lambda\\phi^{4}$ self-interacting theory with a frequency-dependent coupling.

E. Arias; E. Goulart; G. Krein; G. Menezes; N. F. Svaiter

2011-03-18

249

Extended Hamiltonian systems in multisymplectic field theories

We consider Hamiltonian systems in first-order multisymplectic field theories. We review the properties of Hamiltonian systems in the so-called restricted multimomentum bundle, including the variational principle which leads to the Hamiltonian field equations. In an analogous way to how these systems are defined in the so-called extended (symplectic) formulation of nonautonomous mechanics, we introduce Hamiltonian systems in the extended multimomentum bundle. The geometric properties of these systems are studied, the Hamiltonian equations are analyzed using integrable multivector fields, the corresponding variational principle is also stated, and the relation between the extended and the restricted Hamiltonian systems is established. All these properties are also adapted to certain kinds of submanifolds of the multimomentum bundles in order to cover the case of almost-regular field theories.

Echeverria-Enriquez, Arturo; Leon, Manuel de; Munoz-Lecanda, Miguel C.; Roman-Roy, Narciso [Departamento de Matematica Aplicada IV, Campus Norte UPC, Edificio C-3, C/Jordi Girona 1, E-08034 Barcelona (Spain); Instituto de Matematicas y Fisica Fundamental, CSIC, C/Serrano 123, E-28006 Madrid (Spain); Departamento de Matematica Aplicada IV, Campus Norte UPC, Edificio C-3, C/Jordi Girona 1, E-08034 Barcelona (Spain)

2007-11-15

250

Symmetry analysis for anisotropic field theories

The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.

Parra, Lorena; Vergara, J. David [Instituto de Ciencias Nucleares, UNAM, Circuito Exterior s/n, Ciudad Universitaria. Delg. Coyoacan. C.P. 04510 Mexico DF (Mexico)

2012-08-24

251

Continuous wavelet transform in quantum field theory

NASA Astrophysics Data System (ADS)

We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ?4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ?4 theory, consists in substitution of the local fields ?(x) by those dependent on both the position x and the resolution a. The substitution of the action S[?(x)] by the action S[?a(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=??a1(x1)…?an(xn)? finite for any given set of regions by means of an effective cutoff scale A=min?(a1,…,an).

Altaisky, M. V.; Kaputkina, N. E.

2013-07-01

252

Entanglement entropy in scalar field theory

NASA Astrophysics Data System (ADS)

Understanding the dependence of entanglement entropy on the renormalized mass in quantum field theories can provide insight into phenomena such as quantum phase transitions, since the mass varies in a singular way near the transition. Here we perturbatively calculate the entanglement entropy in interacting scalar field theory, focusing on the dependence on the field’s mass. We study ??4 and g?3 theories in their ground state. By tracing over a half space, using the replica trick and position space Green’s functions on the cone, we show that spacetime volume divergences cancel and renormalization can be consistently performed in this conical geometry. We establish finite contributions to the entanglement entropy up to two-loop order, involving a finite area law. The resulting entropy is simple and intuitive: the free theory result in d = 3 (that we included in an earlier publication) ?S ˜ A?m2ln?(m2) is altered, to leading order, by replacing the bare mass m by the renormalized mass mr evaluated at the renormalization scale of zero momentum.

Hertzberg, Mark P.

2013-01-01

253

Prequantum Classical Statistical Field Theory: Fundamentals

We present fundamentals of a prequantum model with hidden variables of the classical field type. In some sense this is the comeback of classical wave mechanics. Our approach also can be considered as incorporation of quantum mechanics into classical signal theory. All quantum averages (including correlations of entangled systems) can be represented as classical signal averages and correlations.

Khrennikov, Andrei [International Center for Mathematical Modelling in Physics and Cognitive Sciences, Linnaeus University, Vaexjoe, S-35195 (Sweden)

2011-03-28

254

Finite size effects in massive field theory

NASA Astrophysics Data System (ADS)

The exponentially small, leading finite size correction to zero momentum, 1PI, propagator amputated, n point vertex functions in a massive field theory is shown to be fixed by two volume independent parameters. The subleading correction is further exponentially suppressed. In contrast, the finite volume constrained effective potential approaches its infinite volume limit with power law corrections.

Neuberger, Herbert

1989-12-01

255

Electromagnetic interactions in Halo Effective Field Theory

After a brief discussion of effective field theory applied to nuclear clusters, I concentrate on the inclusion of two particular aspects, namely, narrow resonances and electromagnetic interactions. As examples of applications, I present the details of our studies on alpha-alpha and proton-alpha scattering.

Renato Higa

2010-01-04

256

Classical Cellular Automata and Quantum Field Theory

It is pointed out that a mathematical relation exists between cellular automata and quantum field theories. Although the proofs are far from perfect, they do suggest a new look at the origin of quantum mechanics, and an essential role for the gravitational force in these considerations is suspected.

Gerard't Hooft

2010-01-01

257

Group Field Theory and Loop Quantum Gravity

We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a perspective on future developments.

Oriti, Daniele

2014-01-01

258

Modular bootstrap in Liouville field theory

The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.

Leszek Hadasz; Zbigniew Jaskolski; Paulina Suchanek

2009-11-22

259

Bound States in Quantum Field Theory

The relativistic two-body equation of Bethe and Salpeter is derived from field theory. It is shown that the Feynman two-body kernel may be written as a sum of wave functions over the states of the system. These wave functions depend exponentially on the energies of the states to which they correspond and therefore provide a means of calculating energy levels

Murray Gell-Mann; Francis Low

1951-01-01

260

Physical properties of quantum field theory measures

NASA Astrophysics Data System (ADS)

Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar-Lewandowski (AL) measure on spaces of connections. In particular we prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar-Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve.

Mourão, J. M.; Thiemann, T.; Velhinho, J. M.

1999-05-01

261

Quasiparticles in Finite-Temperature Field Theory

Conventional finite-temperature perturbation theory in which propagators have poles at $k^{2}=m^{2}$ is shown to break down at the two-loop level for self-interacting scalar fields. The breakdown is avoided by using free thermal propagators that have poles at the same energy as the exact thermal propagator. This quasiparticle energy ${\\cal E}(\\vec{k})$ is temperature-dependent, complex, and gauge invariant. An operator theory containing two self-adjoint scalar fields is presented in which all temperature dependence is incorporated into the Hamiltonian. No thermal traces are required to compute thermal Green functions. Choosing the spectrum of the unperturbed part of the Hamiltonian to contain the exact quasiparticle energy ${\\cal E}(\\vec{k})$ produces a resummed perturbation theory that has the correct poles and branch cuts. The location of the poles and cuts is explained directly in terms of the spectrum of the Hamiltonian.

H. Arthur Weldon

1998-09-10

262

Topics in nonsupersymmetric field theory and string theory

NASA Astrophysics Data System (ADS)

In this two-part thesis, we study various non-supersymmetric aspects of field theory and string theory. In part I, we focus on N = 1 supersymmetric gauge theories. Nonperturbative effects in these theories can spontaneously break supersymmetry, a phenomenon known as dynamical supersymmetry breaking (DSB). Motivated by the search for simpler models of DSB, we explore the (phenomenologically viable) possibility that the non-supersymmetric vacuum is only meta-stable. We find that meta-stable DSB occurs in a surprisingly simple class of models: N = 1 supersymmetric QCD, with massive flavors. We also discuss how various model building challenges, such as large flavor symmetries and the absence of an R-symmetry, can be easily accommodated in these theories. In part II, we switch gears to study a class of non-supersymmetric string theories known (p, q) minimal string theories. These models describe strings propagating in a d < 2 dimensional target space. Although they are exactly solvable, they nevertheless provide a rich source of stringy phenomena, including D-branes, open/closed duality, and holography. In chapter 5, we analyze the D-branes of the minimal string. We show how an auxiliary Riemann surface emerges from the D-branes and provides a unified geometric description of all of these theories. In chapter 6, we compute the annulus amplitudes between different types of branes and show how they fit into the geometrical framework. Finally, in chapter 7 we study the target space of the minimal string, using the D-branes as probes. We find that target space is drastically modified by nonperturbative quantum effects, and we discuss the possible implications of this for topological strings and black holes.

Shih, David

263

Weighting bubbles in group field theory

NASA Astrophysics Data System (ADS)

Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the bubbles of the graphs in the Feynman evaluations. In dimension three, our model exhibits new symmetries, interpreted as the action of the vertex translations of the triangulation. The extra field indices have an elegant algebraic interpretation: they encode the structure of a semisimple algebra. Remarkably, when the algebra is chosen to be associative, the new structure contributes a topological invariant from each bubble of the graph to the Feynman amplitudes.

Baratin, Aristide; Freidel, Laurent; Gurau, Razvan

2014-07-01

264

Weighting bubbles in group field theory

Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the bubbles of the graphs in the Feynman evaluations. In dimension three, our model exhibits new symmetries, interpreted as the action of the vertex translations of the triangulation. The extra field indices have an elegant algebraic interpretation: they encode the structure of a semi-simple algebra. Remarkably, when the algebra is chosen to be associative, the new structure contributes a topological invariant from each bubble of the graph to the Feynman amplitudes.

Aristide Baratin; Laurent Freidel; Razvan Gurau

2014-05-12

265

Topological Field Theories in 2 dimensions Constantin Teleman

Topological Field Theories in 2 dimensions Constantin Teleman UC Berkeley Amsterdam, 14 July 2008 Constantin Teleman 2D Topological Field Theories #12;Origins The notion of a Topological Field Theory (TFT space). This space of fields is "multiplicative in pieces of X". Constantin Teleman 2D Topological Field

Teleman, Constantin

266

Quantum stability of chameleon field theories.

Chameleon scalar fields are dark-energy candidates which suppress fifth forces in high density regions of the Universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound m<0.0073(?/10 g cm(-3))(1/3) eV for gravitational-strength coupling whereas fifth force experiments place a lower bound of m>0.0042 eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential. PMID:23006073

Upadhye, Amol; Hu, Wayne; Khoury, Justin

2012-07-27

267

In this thesis, the author presents some works in the direction of studying quantum effects in locally supersymmetric effective field theories that appear in the low energy limit of superstring theory. After reviewing the Kaehler covariant formulation of supergravity, he shows the calculation of the divergent one-loop contribution to the effective boson Lagrangian for supergravity, including the Yang-Mills sector and the helicity-odd operators that arise from integration over fermion fields. The only restriction is on the Yang-Mills kinetic energy normalization function, which is taken diagonal in gauge indices, as in models obtained from superstrings. He then presents the full result for the divergent one-loop contribution to the effective boson Lagrangian for supergravity coupled to chiral and Yang-Mills supermultiplets. He also considers the specific case of dilaton couplings in effective supergravity Lagrangians from superstrings, for which the one-loop result is considerably simplified. He studies gaugino condensation in the presence of an intermediate mass scale in the hidden sector. S-duality is imposed as an approximate symmetry of the effective supergravity theory. Furthermore, the author includes in the Kaehler potential the renormalization of the gauge coupling and the one-loop threshold corrections at the intermediate scale. It is shown that confinement is indeed achieved. Furthermore, a new running behavior of the dilaton arises which he attributes to S-duality. He also discusses the effects of the intermediate scale, and possible phenomenological implications of this model.

Saririan, K.

1997-05-01

268

Conservation laws. Generation of physical fields. Principles of field theories

In the paper the role of conservation laws in evolutionary processes, which proceed in material systems (in material media) and lead to generation of physical fields, is shown using skew-symmetric differential forms. In present paper the skew-symmetric differential forms on deforming (nondifferentiable) manifolds were used in addition to exterior forms, which have differentiable manifolds as a basis. Such skew-symmetric forms (which were named evolutionary ones since they possess evolutionary properties), as well as the closed exterior forms, describe the conservation laws. But in contrast to exterior forms, which describe conservation laws for physical fields, the evolutionary forms correspond to conservation laws for material systems. The evolutionary forms possess an unique peculiarity, namely, the closed exterior forms are obtained from these forms. It is just this that enables one to describe the process of generation of physical fields, to disclose connection between physical fields and material systems and to resolve many problems of existing field theories.

L. I. Petrova

2007-04-19

269

Dirac quantization of parametrized field theory

Parametrized field theory (PFT) is free field theory on flat spacetime in a diffeomorphism invariant disguise. It describes field evolution on arbitrary (and in general, curved) foliations of the flat spacetime instead of only the usual flat foliations, by treating the 'embedding variables' which describe the foliation as dynamical variables to be varied in the action in addition to the scalar field. A formal Dirac quantization turns the constraints of PFT into functional Schroedinger equations which describe evolution of quantum states from an arbitrary Cauchy slice to an infinitesimally nearby one. This formal Schroedinger picture-based quantization is unitarily equivalent to the standard Heisenberg picture-based Fock quantization of the free scalar field if scalar field evolution along arbitrary foliations is unitarily implemented on the Fock space. Torre and Varadarajan (TV) showed that for generic foliations emanating from a flat initial slice in spacetimes of dimension greater than 2, evolution is not unitarily implemented, thus implying an obstruction to Dirac quantization. We construct a Dirac quantization of PFT, unitarily equivalent to the standard Fock quantization, using techniques from loop quantum gravity (LQG) which are powerful enough to supercede the no-go implications of the TV results. The key features of our quantization include an LQG type representation for the embedding variables, embedding-dependent Fock spaces for the scalar field, an anomaly free representation of (a generalization of) the finite transformations generated by the constraints, and group averaging techniques. The difference between the 1+1-dimensional case and the case of higher spacetime dimensions is that for the latter, only finite gauge transformations are defined in quantum theory, not the infinitesimal ones.

Varadarajan, Madhavan [Raman Research Institute, Bangalore 560 080 (India)

2007-02-15

270

Noether symmetries, energy-momentum tensors, and conformal invariance in classical field theory

In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. With this baggage on board, we next discuss in detail, for Poincare invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincare symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincare. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincare invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved background.

Pons, Josep M. [Departament ECM and ICC, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia (Spain)

2011-01-15

271

Relative entropies in conformal field theory.

Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance. PMID:25126908

Lashkari, Nima

2014-08-01

272

Nuclear effective field theory on the lattice

In the low-energy region far below the chiral symmetry breaking scale (which is of the order of 1 GeV) chiral perturbation theory provides a model-independent approach for quantitative description of nuclear processes. In the two- and more-nucleon sector perturbation theory is applicable only at the level of an effective potential which serves as input in the corresponding dynamical equation. To deal with the resulting many-body problem we put chiral effective field theory (EFT) on the lattice. Here we present the results of our lattice EFT study up to next-to-next-to-leading order in the chiral expansion. Accurate description of two-nucleon phase-shifts and ground state energy ratio of dilute neutron matter up to corrections of higher orders shows that lattice EFT is a promising tool for a quantitative description of low-energy few- and many-body systems.

Hermann Krebs; Bugra Borasoy; Evgeny Epelbaum; Dean Lee; Ulf-G. Meiß ner

2008-10-01

273

Vortex operators in gauge field theories

Several related aspects of the 't Hooft vortex operator are studied. The current picture of the vacuum of quantum chromodynamics, the idea of dual field theories, and the idea of the vortex operator are reviewed first. The Abelian vortex operator written in terms of elementary fields and the calculation of its Green's functions are considered. A two-dimensional solvable model of a Dirac string is presented. The expression of the Green's functions more neatly in terms of Wu and Yang's geometrical idea of sections is addressed. The renormalization of the Green's functions of two kinds of Abelian looplike operators, the Wilson loop and the vortex operator, is studied; for both operators only an overall multiplicative renormalization is needed. In the case of the vortex this involves a surprising cancellation. Next, the dependence of the Green's functions of the Wilson and 't Hooft operators on the nature of the vacuum is discussed. The cluster properties of the Green's functions are emphasized. It is seen that the vortex operator in a massive Abelian theory always has surface-like clustering. The form of Green's functions in terms of Feynman graphs is the same in Higgs and symmetric phases; the difference appears in the sum over all tadpole trees. Finally, systems having fields in the fundamental representation are considered. When these fields enter only weakly into the dynamics, a vortex-like operator is anticipated. Any such operator can no longer be local looplike, but must have commutators at long range. A U(1) lattice gauge theory with two matter fields, one singly charged (fundamental) and one doubly charged (adjoint), is examined. When the fundamental field is weakly coupled, the expected phase transitions are found. When it is strongly coupled, the operator still appears to be a good order parameter, a discontinuous change in its behavior leads to a new phase transition. 18 figures.

Polchinski, J.

1980-07-01

274

Advances in mean-field dynamo theories

NASA Astrophysics Data System (ADS)

We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We give an example of the mean-field solar dynamo model that incorporates the fairly complete expressions for the mean-electromotive force, the subsurface shear layer and the conservation of the total helicity. The model is used to shed light on the issues in the solar dynamo and on the future development of this field of research.

Pipin, V. V.

2013-07-01

275

New Numerical Method for Fermion Field Theory

A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using Grassmann polynomial expansions for the generating functional $Z$, we calculate propagators for systems of interacting fermions. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. Because it is not based on a statistical technique, it does not have many of the difficulties often encountered when simulating fermions. Since no determinant is ever calculated, solutions to problems with dynamical fermions are handled more easily. This approach is very flexible, and can be taylored to specific problems based on convenience and computational constraints. We present simple examples to illustrate the method; more general schemes are desirable for more complicated systems.

John W. Lawson; G. S. Guralnik

1995-07-25

276

Holographic Gauge Theory with Maxwell Magnetic Field

We first apply the transformation of mixing azimuthal with wrapped coordinate to the 11D M-theory with a stack N M5-branes to find the spacetime of a stack of N D4-branes with magnetic field in 10D IIA string theory, after the Kaluza-Klein reduction. In the near-horizon limit the background becomes the Melvin magnetic field deformed $AdS_6 \\times S^4$. Although the solution represents the D-branes under the Melvin RR one-form we use a simple observation to see that it also describes the solution of D-branes under the Maxwell magnetic field. As the magnetic field we consider is the part of the background itself we have presented an alternative to previous literature, because our method does not require the assumption of negligible back reaction. Next, we use the found solution to investigate the meson property through D4/D8 system (Sakai-Sugimoto model) and compare it with those studied by other authors. Finally, we present a detailed analysis about the Wilson loop therein and results show that the external Maxwell magnetic field will enhance the quark-antiquark potential.

Wung-Hong Huang

2009-04-15

277

Field theory in condensed matter physics

Field theory, born as a description of high energy physics, is also used at much lower energies, in condensed matter physics and statistical mechanics. \\\\Ve make a historical survey oC haw this usage cvolvcd, fram the Dirac equation to the presento RESU~tEN. La teoría de campo, inicialmente utilizada en la física de altas energías, se usa también a mucho más

CARLOS A. A. DE

278

The Global Approach to Quantum Field Theory

Bryce Seligman DeWitt (1923–2004), a friend and mentor to many, was a towering figure in the development of the quantum theories of gravity and gauge fields. To appreciate his uniqueness, one must recall the history through which he lived. From DeWitt's birth date through 1965, general relativity (GR) was considered to have so few empirically testable predictions that its practitioners

S A Fulling

2006-01-01

279

Modified Hamiltonian formalism for higher-derivative theories

An alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach, it has the following advantages: (i) The Lagrangian, when expressed in terms of new variables, yields proper equations of motion; no additional Lagrange multipliers are necessary. (ii) The Legendre transformation can be performed in a straightforward way, provided the Lagrangian is nonsingular in the Ostrogradski sense. The generalizations to singular Lagrangians as well as field theory are presented.

Andrzejewski, K.; Gonera, J.; Machalski, P.; Maslanka, P. [Department of Theoretical Physics II, University of Lodz, Pomorska 149/153, 90-236 Lodz (Poland)

2010-08-15

280

Theory of Classical Higgs Fields. I. Matter Fields

Higgs fields are attributes of classical gauge theory on a principal bundle $P\\to X$ whose structure Lie group $G$ if is reducible to a closed subgroup $H$. They are represented by sections of the quotient bundle $P/H\\to X$. A problem lies in description of matter fields with an exact symmetry group $H$. They are represented by sections of a composite bundle which is associated to an $H$-principal bundle $P\\to P/H$. It is essential that they admit an action of a gauge group $G$.

G. Sardanashvily; A. Kurov

2013-12-13

281

A novel string field theory solving string theory by liberating left and right movers

NASA Astrophysics Data System (ADS)

We put forward ideas to a novel string field theory based on making some "objects" that essentially describe "liberated" left- and right- mover fields ( ? + ?) and ( ? - ?) on the string. Our novel string field theory is completely definitely different from any other string theory in as far as a "null set" of information in the string field theory Fock space has been removed relatively, to the usual string field theories. So our theory is definitely new. The main progress is that we manage to make our novel string field theory provide the correct mass square spectrum for the string. We finally suggest how to obtain the Veneziano amplitude in our model.

Nielsen, Holger B.; Ninomiya, Masao

2014-05-01

282

Lagrangian formulation of Newtonian cosmology

In this paper, we use the Lagrangian formalism of classical mechanics and some assumptions to obtain cosmological differential equations analogous to Friedmann and Einstein equations, obtained from the theory of general relativity. This method can be used to a universe constituted of incoherent matter, that is, the cosmologic substratum is comprised of dust.

H. S. Vieira; V. B. Bezerra

2014-01-25

283

Quasiparticle excitations in relativistic quantum field theory

We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.

Daniel Arteaga

2008-01-28

284

Aspects of Four Dimensional N = 2 Field Theory

superconformal quiver gauge theory by putting regular singularity at the puncture. The algorithm of calculating weakly coupled gauge group in any duality frame is developed. The asymptotical free theory and Argyres-Douglas field theory can also be constructed...

Xie, Dan

2011-07-11

285

Non-topological solitons in field theories with kinetic self-coupling

We investigate some fundamental features of a class of non-linear relativistic lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space dimensions which are finite-energy and stable. We determine general conditions for the existence and stability of these non-topological soliton solutions. In particular, we perform a linear stability analysis that goes beyond the usual Derrick-like criteria. On the basis of these considerations we obtain a complete characterization of the soliton-supporting members of the aforementioned class of non-linear field theories. We then classify the family of soliton-supporting theories according to the central and asymptotic behaviors of the soliton field, and provide illustrative explicit examples of models belonging to each of the corresponding sub-families. In the present work we restrict most of our considerations to one and many-components scalar models. We show that in these cases the finite-energy static spherically symmetric solutions are stable against charge-preserving perturbations, provided that the vacuum energy of the model vanishes and the energy density is positive definite. We also discuss briefly the extension of the present approach to models involving other types of fields, but a detailed study of this more general scenario will be addressed in a separate publication.

Joaquin Diaz-Alonso; Diego Rubiera-Garcia

2007-05-01

286

On conformal field theories with extremal values

NASA Astrophysics Data System (ADS)

Unitary conformal field theories (CFTs) are believed to have positive (non-negative) energy correlators. Energy correlators are universal observables in higher-dimensional CFTs built out of integrated Wightman functions of the stress-energy tensor. We analyze energy correlators in parity invariant four-dimensional CFTs. The goal is to use the positivity of energy correlators to further constrain unitary CFTs. It is known that the positivity of the simplest one-point energy correlator implies that where a and c are the Weyl anomaly coefficients. We use the positivity of higher point energy correlators to show that CFTs with extremal values of have trivial scattering observables. More precisely, for and all energy correlators are fixed to be the ones of the free boson and the free vector theory correspondingly. Similarly, we show that the positivity and finiteness of energy correlators together imply that the three-point function of the stress tensor in a CFT cannot be proportional to the one in the theory of free boson, free fermion or free vector field.

Zhiboedov, Alexander

2014-04-01

287

Physics 221B: Solution to HW # 8 Quantum Field Theory

Physics 221B: Solution to HW # 8 Quantum Field Theory 1) Bosonic Grand-Partition Function The solution to this problem is outlined clearly in the beginning of the lecture notes `Quantum Field Theory II

Murayama, Hitoshi

288

FROM CLASSICAL THETA FUNCTIONS TO TOPOLOGICAL QUANTUM FIELD THEORY

FROM CLASSICAL THETA FUNCTIONS TO TOPOLOGICAL QUANTUM FIELD THEORY RAZVAN GELCA AND ALEJANDRO URIBE Abstract. Abelian Chern-Simons theory relates classical theta func- tions to the topological quantum field Chern-Simons theory directly from the theory of classical theta func- tions. It turns out

Gelca, Razvan

289

The effective field theory treatment of quantum gravity

This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.

Donoghue, John F. [Department of Physics, University of Massachusetts, Amherst, MA 01003 (United States)

2012-09-24

290

Lattice field theory simulations of graphene

We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling.

Joaquín E. Drut; Timo A. Lähde

2009-01-06

291

Heterotic $?$'-corrections in Double Field Theory

We extend the generalized flux formulation of Double Field Theory to include all the first order bosonic contributions to the $\\alpha '$ expansion of the heterotic string low energy effective theory. The generalized tangent space and duality group are enhanced by $\\alpha'$ corrections, and the gauge symmetries are generated by the usual (gauged) generalized Lie derivative in the extended space. The generalized frame receives derivative corrections through the spin connection with torsion, which is incorporated as a new degree of freedom in the extended bein. We compute the generalized fluxes and find the Riemann curvature tensor with torsion as one of their components. All the four-derivative terms of the action, Bianchi identities and equations of motion are reproduced. Using this formalism, we obtain the first order $\\alpha'$ corrections to the heterotic Buscher rules. The relation of our results to alternative formulations in the literature is discussed and future research directions are outlined.

Oscar A. Bedoya; Diego Marques; Carmen Nunez

2014-07-01

292

Working Group Report: Lattice Field Theory

This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.

Blum, T.; et al.,

2013-10-22

293

Even symplectic supermanifolds and double field theory

Over many decades, the word "double" has appeared in various contexts, at times seemingly unrelated. Several have some relation to mathematical physics. Recently, this has become particularly strking in DFT (double field theory). Two 'doubles' that are particularly relevant are double vector bundles and Drinfel'd doubles. The original Drinfel'd double occurred in the contexts of quantum groups and of Lie bialgebras. Quoting T. Voronov: "Double Lie algebroids arose in the works on double Lie groupoids and in connection with an analog for Lie bialgebroids of the classical Drinfel'd double of Lie bialgebras...Suppose $(A,A^*)$ is a Lie bialgebroid over a base $M$... Mackenzie and Roytenberg suggested two different constructions based on the cotangent bundles $T^*A$ and $T^*\\Pi A$, respectively. Here $\\Pi$ is the fibre-wise parity reversal functor." Although the approaches of Roytenberg and of Mackenzie look very different, Voronov establishes their equivalence. We have found Roytenberg's version to be quite congenial with our attempt to interpret the gauge algebra of DFT in terms of Poisson brackets on a suitable generalized Drinfel'd double. This double of a Lie bialgebroid $(A,A^*)$ provides a framework to describe the differentials of $A$ and $A^*$ on an equal footing as Hamiltonian functions on an even symplectic supermanifold. A special choice of momenta explicates the double coordinates of DFT and shows their relation to the strong constraint determining the physical fields of double field theory.

Andreas Deser; Jim Stasheff

2014-06-13

294

The effective field theory of dark energy

We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.

Gubitosi, Giulia; Vernizzi, Filippo [CEA, IPhT, 91191 Gif-sur-Yvette cédex (France); Piazza, Federico, E-mail: giulia.gubitosi@roma1.infn.it, E-mail: fpiazza@apc.univ-paris7.fr, E-mail: filippo.vernizzi@cea.fr [Paris Center for Cosmological Physics (PCCP) and Laboratoire APC, Université Paris 7, 75205 Paris (France)

2013-02-01

295

The clebsch potential approach to fluid lagrangians

The clebsch potential approach to fluid lagrangians is developed in order to establish contact with other approaches to fluids. Three variants of the perfect fluid approach are looked at. The first is an explicit linear lagrangian constructed directly from the clebsch potentials, this has fixed equation of state and explicit expression for the pressure but is less general than a perfect fluid. The second is lagrangians more general than that of a perfect fluid which are constructed from higher powers of the comoving vector. The third is lagrangians depending on two vector fields which can represent both density flow and entropy flow.

Mark D. Roberts

2009-10-19

296

Microscopic Fields and Macroscopic Averages in Einstein's Unified Field Theory

The relation between microscopic and macroscopic entities in the generally covariant theories is considered, and it is argued that a sensible definition of the macroscopic averages requires a restriction of the allowed transformations of coordinates. Spacetime averages of the geometric objects of Einstein's unified field theory are then defined, and the reconstruction of some features of macroscopic reality from hypothetic microscopic structures is attempted. It is shown how a fluctuating microscopic behaviour of the metric field can rule the constitutive relation for electromagnetism both in vacuo and in nondispersive material media. Moreover, if both the metric and the skew tensor density that represents the electric displacement and the magnetic field are assumed to possess a wavy microscopic structure, nonvanishing generalized force densities can appear in the continuum. They originate from a resonance process, in which at least three waves need to be involved. This process only occurs if the wavevectors fulfil the three-wave resonance condition, so ubiquitous in quantum physics. The wavy behaviour of the metric is essential for the occurrence of this resonance phenomenon.

S. Antoci

1998-01-15

297

Lagrangian and Hamiltonian Formulation of Plasma Problems.

National Technical Information Service (NTIS)

A systematic formulation of existing theories for classical plasma systems by use of Hamilton's variational principle is presented at the microscopic, kinetic and fluid-model levels of description. Both the Lagrangian and Hamiltonian functions are given f...

G. C. Georges

1969-01-01

298

Ward identities for Lagrangian conformal models.

National Technical Information Service (NTIS)

Some aspects of conformal theories with Lagrangian representation, are discussed. The study is carried out in the framework of formal perturbative series. The development of the concepts and the problems raised, are illustrated by the free bosonic string....

S. Lazzarini, R. Stora

1989-01-01

299

Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean

Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived \\emph{Sargassum} distributions.

F. J. Beron-Vera; M. J. Olascoaga; G. Haller; M. Farazmand; J. Trinanes; Y. Wang

2014-08-27

300

Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean

Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satell...

Beron-Vera, F J; Haller, G; Farazmand, M; Trinanes, J; Wang, Y

2014-01-01

301

Theory of microemulsions in a gravitational field

NASA Technical Reports Server (NTRS)

A theory of microemulsions developed previously is extended to include the effect of a gravitational field. It predicts variation with position of drop size, drop volume fraction, and area per molecule in the surfactant films within a microemulsion phase. Variation in volume fraction is greatest and occurs in such a way that oil content increases with increasing elevation, as has been found experimentally. Large composition variations are predicted within a middle phase microemulsion near optimal conditions because inversion from the water-continuous to the oil-continuous arrangement occurs with increasing elevation. Generally speaking, gravity reduces solubilization within microemulsions and promotes separation of excess phases.

Jeng, J. F.; Miller, Clarence A.

1989-01-01

302

Effective field theory of interacting ? electrons

NASA Astrophysics Data System (ADS)

We develop a ?-electron effective field theory (?-EFT) wherein the two-body Hamiltonian for a ?-electron system is expressed in terms of three effective parameters: the ?-orbital quadrupole moment, the on-site repulsion, and a dielectric constant. As a first application of this ?-EFT, we develop a model of screening in molecular junctions based on image multipole moments, and use this to investigate the reduction of the HOMO-LUMO gap of benzene. Beyond this, we also use ?-EFT to calculate the differential conductance spectrum of the prototypical benzenedithiol-Au single-molecule junction and the ?-electron contribution to the van der Waals interaction between benzene and a metallic electrode.

Barr, J. D.; Stafford, C. A.; Bergfield, J. P.

2012-09-01

303

He??6 in cluster effective field theory

NASA Astrophysics Data System (ADS)

The hypernucleus He??6 is studied as a three-body (???) cluster system in cluster effective field theory at leading order. We find that the three-body contact interaction exhibits the limit cycle when the cutoff in the integral equations is sent to the asymptotic limit and thus it should be promoted to leading order. We also derive a determination equation of the limit cycle which reproduces the numerically obtained limit cycle. We then study the correlations between the double ? separation energy B?? of He??6 and the scattering length a?? of the S-wave ?? scattering. The role of the scale in this approach is also discussed.

Ando, Shung-Ichi; Oh, Yongseok

2014-09-01

304

Quasiparticle Properties in Effective Field Theory

The quasiparticle concept is an important tool for the description of many-body systems. We study the quasiparticle properties for dilute Fermi systems with short-ranged, repulsive interactions using effective field theory. We calculate the proper self-energy contributions at order (K_f/Lambda)^3, where Lambda is the short-distance scale that sets the size of the effective range parameters and K_f the Fermi momentum. The quasiparticle energy, width, and effective mass to order O(K_f/Lambda)^3 are derived from the calculated self-energy.

L. Platter; H. -W. Hammer; Ulf-G. Meißner

2002-08-27

305

Scalar-field theory of dark matter

NASA Astrophysics Data System (ADS)

We develop a theory of dark matter based on a previously proposed picture, in which a complex vacuum scalar field makes the universe a superfluid, with the energy density of the superfluid giving rise to dark energy, and variations from vacuum density giving rise to dark matter. We formulate a nonlinear Klein-Gordon equation to describe the superfluid, treating galaxies as external sources. We study the response of the superfluid to the galaxies, in particular, the emergence of the dark-matter galactic halo, contortions during galaxy collisions and the creation of vortices due to galactic rotation.

Huang, Kerson; Xiong, Chi; Zhao, Xiaofei

2014-05-01

306

Purely cubic action for string field theory

NASA Technical Reports Server (NTRS)

It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.

Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.

1986-01-01

307

Dynamic field theory and equations of motion in cosmology

NASA Astrophysics Data System (ADS)

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast ??/??1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits ??/??1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress-energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.

Kopeikin, Sergei M.; Petrov, Alexander N.

2014-11-01

308

Stochastic inflation and replica field theory

We adopt methods from statistical field theory to stochastic inflation. For the example of a free test field in de Sitter and power-law inflation, the power spectrum of long-wavelength fluctuations is computed. We study its dependence on the shape of the filter that separates long- from short-wavelength modes. While for filters with infinite support the phenomenon of dimensional reductions is found on large superhorizon scales, filters with compact support return a scale-invariant power spectrum in the infrared. Features of the power spectrum, induced by the filter, decay within a few e-foldings. Thus the late-time power spectrum is independent of the filter details.

Kuehnel, Florian; Schwarz, Dominik J. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, 33501 Bielefeld (Germany)

2009-02-15

309

Continuum regularization of quantum field theory

Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.

Bern, Z.

1986-04-01

310

Space-time resolved quantum field theory

NASA Astrophysics Data System (ADS)

We have solved simplified model versions of the time-dependent Dirac and Yukawa equation numerically to study the time evolution of electrons, positrons and photons with full spatial resolution. The goal is to better understand how various particle creation and annihilation processes that require quantum field theory can be visualized. There are many open ended questions that we will address. Are particles and their antimatter companions created instantly, or do they require a certain minimum amount of time? Are they created at precisely the same location? What is the difference between a bare and a physical particle? Forces between two particles are usually understood on a microscopic level as the result of an exchange of bosonic particles. How can the same microscopic exchange mechanism lead to a repulsion as well as an attraction? Do these force intermediating particles ``know'' about the charges of the two interacting particles? How can one visualize this exchange? Does it really make sense to distinguish between virtual and real particles? We also examine how a bare electron can trigger the creation of a cloud of virtual photons around it.[4pt] In collaboration with R. Wagner, Intense Laser Physics Theory Unit, Illinois State University; C. Gerry, Lehman College and ILP-ISU; T. Cheng and Q. Su, Intense Laser Physics Theory Unit, Illinois State University.

Grobe, R.

2009-11-01

311

Perfect magnetohydrodynamics as a field theory

We propose the generally covariant action for the theory of a self-coupled complex scalar field and electromagnetism which by virtue of constraints is equivalent, in the regime of long wavelengths, to perfect magnetohydrodynamics (MHD). We recover from it the Euler equation with Lorentz force, and the thermodynamic relations for a prefect fluid. The equation of state of the latter is related to the scalar field's self potential. We introduce 1+3 notation to elucidate the relation between MHD and field variables. In our approach the requirement that the scalar field be single valued leads to the quantization of a certain circulation in steps of ({Dirac_h}/2{pi}); this feature leads, in the classical limit, to the conservation of that circulation. The circulation is identical to that in Oron's generalization of Kelvin's circulation theorem to perfect MHD; we here characterize the new conserved helicity associated with it. We also demonstrate the existence for MHD of two Bernoulli-like theorems for each spacetime symmetry of the flow and geometry; one of these is pertinent to suitably defined potential flow. We exhibit the conserved quantities explicitly in the case that two symmetries are simultaneously present, and give examples. Also in this case we exhibit a new conserved MHD circulation distinct from Oron's, and provide an example.

Bekenstein, Jacob D.; Betschart, Gerold [Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel)

2006-10-15

312

Refringence, field theory, and normal modes

In a previous paper [gr-qc/0104001; Class. Quant. Grav. 18 (2001) 3595-3610] we have shown that the occurrence of curved spacetime ``effective Lorentzian geometries'' is a generic result of linearizing an arbitrary classical field theory around some non-trivial background configuration. This observation explains the ubiquitous nature of the ``analog models'' for general relativity that have recently been developed based on condensed matter physics. In the simple (single scalar field) situation analyzed in our previous paper, there is a single unique effective metric; more complicated situations can lead to bi-metric and multi-metric theories. In the present paper we will investigate the conditions required to keep the situation under control and compatible with experiment -- either by enforcing a unique effective metric (as would be required to be strictly compatible with the Einstein Equivalence Principle), or at the worst by arranging things so that there are multiple metrics that are all ``close'' to each other (in order to be compatible with the {\\Eotvos} experiment). The algebraically most general situation leads to a physical model whose mathematical description requires an extension of the usual notion of Finsler geometry to a Lorentzian-signature pseudo-Finsler geometry; while this is possibly of some interest in its own right, this particular case does not seem to be immediately relevant for either particle physics or gravitation. The key result is that wide classes of theories lend themselves to an effective metric description. This observation provides further evidence that the notion of ``analog gravity'' is rather generic.

C. Barcelo; S. Liberati; Matt Visser

2001-11-19

313

Structure of Lanczos-Lovelock Lagrangians in critical dimensions

NASA Astrophysics Data System (ADS)

The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D-dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general covariance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension D = 2 m and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in D = 2 m. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, {R ?{-g} = partial_j R^j} for a doublet of functions R j = ( R 0, R 1) which depends only on the metric and its first derivatives. We explicitly construct families of such R j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in D = 4. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.

Yale, Alexandre; Padmanabhan, T.

2011-06-01

314

D-brane field theory on compact spaces

A low-energy field theory is constructed for Dirichlet p-branes in type II string theory on a space which has been toroidally compactified in d transverse dimensions. This field theory is found by taking a Zd quotient of a theory describing a countably infinite set of branes on the covering space. In accordance with T-duality, the resulting theory is equivalent to

Washington Taylor

1997-01-01

315

Compressible Lagrangian hydrodynamics without Lagrangian cells

Traditional Lagrangian hydrodynamic codes for time dependent, compressible, multimaterial problems in two dimensions use the same general method. A Lagrangian mesh is defined, which moves with the fluid and this mesh defines a set of Lagrangian cells. The mass in each cell remains fixed and the motion of the mesh determines the volume and hence the density of each cell. These methods work well until the mesh becomes distorted due to shear or turbulence. Large distortions cause computer codes to quickly grind to a halt. The usual solution to distortion is to ''rezone'' the mesh. Here we move the mesh points artificially so as to reduce distortions and then map the quantities from the old mesh to the new. This results in unwanted diffusion of mass, momentum and energy throughout the mesh. Even with rezoning, few Lagrangian codes can handle more than limited distortions. Recently, what we call ''Free-Lagrangian'' codes have been developed specifically to handle large distortions. These codes, in addition to adjusting the mesh points, can reconnect mesh points, thus creating new cells. While Free-Lagrangian codes can handle virtually any distortion, they are even more diffusive than rezoners. We are trying a different aproach to the problem. We abandon the idea of Lagrangian cells entirely. In the next section we will discuss how the conservation equations can be solved directly without resorting to Lagrangian cells. Next we will give some examples of calculations using this method. Finally, we will give details of the calculational method presently being used.

Clark, R.A.

1985-01-01

316

Some Lagrangians for systems without a Lagrangian

NASA Astrophysics Data System (ADS)

We demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle.

Nucci, M. C.; Leach, P. G. L.

2011-03-01

317

NASA Technical Reports Server (NTRS)

Ozone transport is calculated for steady, dissipative planetary waves using the Eulerian, Lagrangian mean, and residual circulation. A Lagrangian model of parcel dynamics is used to interpret planetary wave-photochemistry interaction. In chemically active regions the mean field ozone changes are found to be significant only where there are large gradients in chemical sources and sinks along parcel trajectories. The largest changes in the mean field are found in the lower stratosphere and are due to the Lagrangian mean advection. When the Lagrangian mean advection is approximated by the residual circulation, errors in the transport velocities as large as 30 pct may occur.

Rood, R. B.; Schoeberl, M. R.

1983-01-01

318

Causality and chance in relativistic quantum field theories

Bell appealed to the theory of relativity in formulating his principle of local causality. But he maintained that quantum field theories do not conform to that principle, even when their field equations are relativistically covariant and their observable algebras satisfy a relativistically motivated microcausality condition. A pragmatist view of quantum theory and an interventionist approach to causation prompt the reevaluation of local causality and microcausality. Local causality cannot be understood as a reasonable requirement on relativistic quantum field theories: it is unmotivated even if applicable to them. But microcausality emerges as a sufficient condition for the consistent application of a relativistic quantum field theory.

Richard Healey

2014-05-13

319

UV/IR duality in noncommutative quantum field theory

We review the construction of renormalizable noncommutative euclidean phi(4)-theories based on the UV/IR duality covariant modification of the standard field theory, and how the formalism can be extended to scalar field theories defined on noncommutative Minkowski space.

Andre Fischer; Richard J. Szabo

2010-01-21

320

Intersecting extended objects in supersymmetric field theories

NASA Astrophysics Data System (ADS)

We show that there are three cases for which the generic intersections of p-dimensional extended object solutions of a supersymmetric field theory in a d-dimensional space-time are stringlike. They are (i) d = 4, p = 2, (ii) d = 6, p = 3 and (iii) d = 10, p = 5. By consideration of the topological charges associated with these objects we obtain a necessary condition for stable stringlike intersections to occur, a condition that is satisfied by the first two cases but not the third, which may have implications for the "heterotic 5-branes" recently discussed by Strominger. For case (i) we show by an analysis of the d = 4 Wess-Zumino model that stringlike intersections of domain walls can indeed occur.

Abraham, E. R. C.; Townsend, P. K.

1991-03-01

321

String Calculus: Conformal Field Theory as a Tool in String Theory

String Calculus: Conformal Field Theory as a Tool in String Theory Emil Martinec Enrico Fermi Inst, in the guise of string theory. String theory promises an elegant synthesis of quan- tum mechanics (algebra in string theory in the description of perturbative string propagation. However, one might believe

Gardel, Margaret

322

Multidimensional wave field signal theory: Mathematical foundations

NASA Astrophysics Data System (ADS)

Many important physical phenomena are described by wave or diffusion-wave type equations. Since these equations are linear, it would be useful to be able to use tools from the theory of linear signals and systems in solving related forward or inverse problems. In particular, the transform domain signal description from linear system theory has shown concrete promise for the solution of problems that are governed by a multidimensional wave field. The aim is to develop a unified framework for the description of wavefields via multidimensional signals. However, certain preliminary mathematical results are crucial for the development of this framework. This first paper on this topic thus introduces the mathematical foundations and proves some important mathematical results. The foundation of the framework starts with the inhomogeneous Helmholtz or pseudo-Helmholtz equation, which is the mathematical basis of a large class of wavefields. Application of the appropriate multi-dimensional Fourier transform leads to a transfer function description. To return to the physical spatial domain, certain mathematical results are necessary and these are presented and proved here as six fundamental theorems. These theorems are crucial for the evaluation of a certain class of improper integrals which arise in the evaluation of inverse multi-dimensional Fourier and Hankel transforms, upon which the framework is based. Subsequently, applications of these theorems are demonstrated, in particular for the derivation of Green's functions in different coordinate systems.

Baddour, Natalie

2011-06-01

323

Quantum field theory and time machines

We analyze the "F-locality condition" (proposed by Kay to be a mathematical implementation of a philosophical bias related to the equivalence principle, we call it the "GH-equivalence principle"), which is often used to build a generalization of quantum field theory to non-globally hyperbolic spacetimes. In particular we argue that the theorem proved by Kay, Radzikowski, and Wald to the effect that time machines with compactly generated Cauchy horizons are incompatible with the F-locality condition actually does not support the "chronology protection conjecture", but rather testifies that the F-locality condition must be modified or abandoned. We also show that this condition imposes a severe restriction on the geometry of the world (it is just this restriction that comes into conflict with the existence of a time machine), which does not follow from the above mentioned philosophical bias. So, one need not sacrifice the GH-equivalence principle to "emend" the F-locality condition. As an example we consider a particular modification, the "MF-locality condition". The theory obtained by replacing the F-locality condition with the MF-locality condition possesses a few attractive features. One of them is that it is consistent with both locality and the existence of time machines.

S. Krasnikov

1998-02-03

324

Source Galerkin Calculations in Scalar Field Theory

In this paper, we extend previous work on scalar $\\phi^4$ theory using the Source Galerkin method. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using polynomial expansions for the generating functional $Z$, we calculate propagators and mass-gaps for a number of systems. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. The use of polynomial expansions illustrates in a clear and simple way the ideas of the Source Galerkin method. But at the same time, this choice has serious limitations. Even after exploiting symmetries, the size of calculations become prohibitive except for small systems. The calculations in this paper were made on a workstation of modest power using a fourth order polynomial expansion for lattices of size $8^2$,$4^3$,$2^4$ in $2D$, $3D$, and $4D$. In addition, we present an alternative to the Galerkin procedure that results in sparse matrices to invert.

John W. Lawson; G. S. Guralnik

1995-07-25

325

Convergent perturbative nuclear effective field theory

We consider the nuclear effective field theory including pions in the two-nucleon sector in the S waves up to including the next-to-next-to-leading order (NNLO) terms according to the power counting suggested by the Wilsonian renormalization group analysis done in a previous paper. We treat only the leading contact interaction nonperturbatively, and the rest, including the long-distance part of pion exchange, are treated as perturbations. To define the long-distance part, it is important to introduce a separation scale, or a cutoff. We employ a hybrid regularization, in which the loops with only contact interactions are regularized with Power Divergence Subtraction (PDS), while the loops with (long-distance part of) pion exchange are regularized with a Gaussian damping factor (GDF), to simplify the (nonperturbative) leading-order amplitudes. The scale introduced by PDS is identified with the cutoff of GDF up to a numerical factor. We emphasize that the introduction of the GDF requires a careful definition of the coupling constant for the pion exchange. We obtain the analytic expressions for the phase shifts for the $^1S_0$ and $^3S_1$-$^3D_1$ channels. By fitting them to the Nijmegen partial wave analysis data, it is shown that the effective theory expansion with perturbative long-distance part of pion exchange is converging.

Koji Harada; Hirofumi Kubo; Tatsuya Sakaeda; Yuki Yamamoto

2013-11-13

326

Hamiltonian constraint in polymer parametrized field theory

NASA Astrophysics Data System (ADS)

Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type “polymer” representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.

Laddha, Alok; Varadarajan, Madhavan

2011-01-01

327

Hamiltonian constraint in polymer parametrized field theory

Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.

Laddha, Alok [Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, Pennsylvania 16802-6300 (United States); Chennai Mathematical Institute, SIPCOT IT Park, Padur PO, Siruseri 603103 (India); Raman Research Institute, Bangalore-560 080 (India); Varadarajan, Madhavan [Raman Research Institute, Bangalore-560 080 (India)

2011-01-15

328

Theory of Electromagnetic Field Measurement and Photoelectron Counting

A theory of electromagnetic field measurement by means of photoionization is developed and applied to photoelectron counting. A probability theory involving multitime joint probability functions for a sequence of photoionizations is formulated. A general quantum-theory definition is proposed for the nonexclusive probability function which occurs in the probability theory. Approximations are then introduced to derive expressions for this probability function

P. L. Kelley; W. H. Kleiner

1964-01-01

329

FROM CLASSICAL THETA FUNCTIONS TO TOPOLOGICAL QUANTUM FIELD THEORY

FROM CLASSICAL THETA FUNCTIONS TO TOPOLOGICAL QUANTUM FIELD THEORY R â?? AZVAN GELCA AND ALEJANDRO URIBE Abstract. Abelian ChernÂSimons theory relates classical theta funcÂ tions to the topological of abelian ChernÂSimons theory directly from the theory of classical theta funcÂ tions. It turns out

Gelca, Razvan

330

The IR-resummed Effective Field Theory of Large Scale Structures

We present a new method to resum the effect of large scale motions in the Effective Field Theory of Large Scale Structures. Because the linear power spectrum in $\\Lambda$CDM is not scale free the effects of the large scale flows are enhanced. Although previous EFT calculations of the equal-time density power spectrum at one and two loops showed a remarkable agreement with numerical results, they also showed a 2% residual which appeared related to the BAO oscillations. We show that this was indeed the case, explain the physical origin and show how a Lagrangian based calculation removes this differences. We propose a simple method to upgrade existing Eulerian calculations to effectively make them Lagrangian and compare the new results with existing fits to numerical simulations. Our new two-loop results agrees with numerical results up to $k\\sim 0.6 h/$Mpc to within 1% with no oscillatory residuals. We also compute power spectra involving momentum which is significantly more affected by the large scale flows. We show how keeping track of these velocities significantly enhances the UV reach of the momentum power spectrum in addition to removing the BAO related residuals. We compute predictions for the real space correlation function around the BAO scale and investigate its sensitivity to the EFT parameters and the details of the resummation technique.

Leonardo Senatore; Matias Zaldarriaga

2014-04-23

331

Structure Constants and Conformal Bootstrap in Liouville Field Theory

An analytic expression is proposed for the three-point function of the exponential fields in the Liouville field theory on a sphere. In the classical limit it coincides with what the classical Liouville theory predicts. Using this function as the structure constant of the operator algebra we construct the four-point function of the exponential fields and verify numerically that it satisfies

A. B. Zamolodchikov; B. Zamolodchikov

332

Short-range entanglement and invertible field theories

Quantum field theories with an energy gap can be approximated at long-range by topological quantum field theories. The same should be true for suitable condensed matter systems. For those with short range entanglement (SRE) the effective topological theory is invertible, and so amenable to study via stable homotopy theory. This leads to concrete topological invariants of gapped SRE phases which are finer than existing invariants. Computations in examples demonstrate their effectiveness.

Freed, Daniel S

2014-01-01

333

Short-range entanglement and invertible field theories

Quantum field theories with an energy gap can be approximated at long-range by topological quantum field theories. The same should be true for suitable condensed matter systems. For those with short range entanglement (SRE) the effective topological theory is invertible, and so amenable to study via stable homotopy theory. This leads to concrete topological invariants of gapped SRE phases which are finer than existing invariants. Computations in examples demonstrate their effectiveness.

Daniel S. Freed

2014-06-27

334

Reggeon Field Theory for Large Pomeron Loops

We analyze the range of applicability of the high energy Reggeon Field Theory $H_{RFT}$ derived in [1]. We show that this theory is valid as long as at any intermediate value of rapidity $\\eta$ throughout the evolution at least one of the colliding objects is dilute. Importantly, at some values of $\\eta$ the dilute object could be the projectile, while at others it could be the target, so that $H_{RFT}$ does not reduce to either $H_{JIMWLK}$ or $H_{KLWMIJ}$. When both objects are dense, corrections to the evolution not accounted for in [1] become important. The same limitation applies to other approaches to high energy evolution available today, such as for example [3] and [4]. We also show that, in its regime of applicability $H_{RFT}$ can be simplified. We derive the simpler version of $H_{RFT}$ and in the large $N_c$ limit rewrite it in terms of the Reggeon creation and annihilation operators. The resulting $H_{RFT}$ is explicitly self dual and provides the generalization of the Pomeron calculus developed in [4] by including higher Reggeons in the evolution. It is applicable for description of `large' Pomeron loops, namely Reggeon graphs where all the splittings occur close in rapidity to one dilute object (projectile), while all the merging close to the other one (target). Additionally we derive, in the same regime expressions for single and double inclusive gluon production (where the gluons are not separated by a large rapidity interval) in terms of the Reggeon degrees of freedom.

Tolga Altinoluk; Alex Kovner; Eugene Levin; Michael Lublinsky

2014-01-29

335

Compressible Lagrangian hydrodynamics without Lagrangian cells

The formulation normally used to calculate compressible Lagrangian hydrodynamics in two dimensions is the following. First define a two-dimensional mesh containing a set of Lagrangian cells. Assign each cell a fixed mass. Compute the acceleration of the mesh points and move the points. The volume of the cell changes with the motion of the points. The changes in cell density, energy, and pressure are computed from the changes in volume. Difficulties occur when there are large distortions in the flow that cause similar large distortions in the Lagrangian cells. The usual solution is to somehow adjust the mesh as the calculation proceeds. This involves either moving individual mesh points or actually reconnecting the mesh. In either case, it becomes necessary to remap the mass from the old cells to the new. This necessarily produces some amount of undesirable numerical diffusion. When and how to adjust the mesh and how to accurately remap the mass and other variables so as to minimize numerical diffusion are the problems. One way to eliminate these problems is to abandon the idea of the Lagrangian cell since it is the distortion of the Lagrangian cell that is the cause of all the other problems. We discuss how the conservation equations can be solved directly without resorting to Lagrangian cells, and we give some examples of calculations using this method. Finally, we give details of the calculational method presently being used.

Clark, R.A.

1985-01-01

336

Gravitational consequences of modern field theories

NASA Technical Reports Server (NTRS)

Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.

Horowitz, Gary T.

1989-01-01

337

A Deformed Poincare Invariance for Group Field Theories

In the context of quantum gravity, group field theories are field theories that generate spinfoam amplitudes as Feynman diagrams. They can be understood as generalizations of the matrix models used for 2d quantum gravity. In particular Boulatov's theory reproduces the amplitudes of the Ponzano-Regge spinfoam model for 3d quantum gravity. Motivated by recent works on field theories on non-commutative flat spaces, we show that Boulatov's theory (and its colored version) is actually invariant under a global deformed Poincare symmetry. This allows to define a notion of flat/excited geometry states when considering scalar perturbations around classical solutions of the group field equations of motion. As a side-result, our analysis seems to point out that the notion of braiding of group field theories should be a key feature to study further in this context.

Florian Girelli; Etera R. Livine

2010-01-17

338

Gravitational Descendants in Symplectic Field Theory

NASA Astrophysics Data System (ADS)

It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov and Pandharipande (Ann Math 163(2):517-560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak and Latschev (

Fabert, Oliver

2011-02-01

339

This paper attempts to analyze central place theory of spatial economics based on supply and demand theory in microeconomics and field theory in physics, and also discuss their relationship. Three most important research findings are described below. Firstly, the concept of market equilibrium could be expressed in the mathematical form of physics field theory under proper hypothesis. That is because the most important aspect of field theory model is that complex analysis is taken as a key mathematical tool. If assuming that imaginary part is neglected in this model, it is found that this model has the same mathematical structure as supply and demand theory of microeconomics. Secondly, the mathematical model of field theory can be applied to express clearly many concepts of central place theory, or even introduce many new concepts. Thirdly, it could also be taken as a study of combining the Hotelling Model and Moses Model for the location theory in another mathematic approach.

Benjamin Chih-Chien Nien

2006-10-11

340

17.418 Field Seminar: International Relations Theory, Spring 2009

This seminar provides an overview of the field of international relations. Each week, a different approach to explaining international relations will be examined. By surveying major concepts and theories in the field, the ...

Fravel, M. Taylor

341

The gauge algebra of double field theory and Courant brackets

We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are constrained fields on the ...

Hull, Chris

342

Homogeneous Rolling Tachyons in Boundary String Field Theory

We study decay of a flat unstable D$p$-brane in the context of boundary string field theory action. Three types of homogeneous rolling tachyons are obtained without and with Born-Infeld type electromagnetic field.

Akira Ishida; Yoonbai Kim; Seyen Kouwn

2006-01-27

343

Electroweak processes of the deuteron in effective field theory

We review our recent calculations of electroweak processes involving the deuteron, based on pionless effective field theory with dibaryon fields. These calculations are concerned with neutron-neutron fusion and np -> d gamma at BBN energies.

Shung-ichi Ando

2005-09-23

344

Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory

An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's

Carl M. Bender; S. P. Klevansky

2010-01-01

345

From Quantum Gravity to Quantum Field Theory via Noncommutative Geometry

A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The interaction involves flux tubes of the gravitational field. In the additional limit where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges.

Johannes Aastrup; Jesper M. Grimstrup

2011-05-01

346

From Quantum Gravity to Quantum Field Theory via Noncommutative Geometry

A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The interaction involves flux tubes of the gravitational field. In the additional limit where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges.

Aastrup, Johannes

2011-01-01

347

From quantum gravity to quantum field theory via noncommutative geometry

NASA Astrophysics Data System (ADS)

A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction, which encodes the kinematics of quantum gravity, we construct semi-classical states which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The emergent interaction involves flux tubes of the gravitational field. In the additional limit, where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges.

Aastrup, Johannes; Møller Grimstrup, Jesper

2014-02-01

348

Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory

NASA Astrophysics Data System (ADS)

We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.

Manuel, Cristina; Torres-Rincon, Juan M.

2014-10-01

349

Helmholtz decomposition of the Lagrangian displacement

NASA Astrophysics Data System (ADS)

Lagrangian displacement field ? is the central object in Lagrangian perturbation theory (LPT). LPT is very successful at high redshifts, but it performs poorly at low redshifts due to severe shell crossing. To understand and quantify the effects of shell crossing, we extract ? from N-body simulation and decompose it into scalar and vector parts. We find that at late time the power spectrum of the scalar part agrees with 1-loop results from LPT at large scales, while the power in small scales is much suppressed due to shell crossing. At z =0, the power spectrum of ? is 10% lower than the 1-loop results at k =0.1 Mpc-1h. Shell crossing also generates the vector contribution in ?, although its effect is subdominant in comparison with the power suppression in the scalar part. At z =0, the vector part contributes 10% to the total power spectrum of ? at k =1 Mpc-1h, while only 1% is expected from the vector contribution in LPT. We also examine the standard LPT recipes and some of its variants. In one of the variants, we include a power suppression factor in the displacement potential to take into account the power suppression in small scales after shell crossing. However, these simple phenomenological approaches are found to yield limited improvement compared to the standard LPT after the onset of shell crossing.

Chan, Kwan Chuen

2014-04-01

350

General physics motivations for numerical simulations of quantum field theory

In this introductory article a brief description of Quantum Field Theories (QFT) is presented with emphasis on the distinction between strongly and weakly coupled theories. A case is made for using numerical simulations to solve QCD, the regnant theory describing the interactions between quarks and gluons. I present an overview of what these calculations involve, why they are hard, and

Rajan Gupta

1999-01-01

351

Lattice p-Form Electromagnetism and Chain Field Theory

Since Wilson's work on lattice gauge theory in the 1970s, discrete versions of field theories have played a vital role in fundamental physics. But there is recent interest in certain higher dimensional analogues of gauge theory, such as p-form electromagnetism, including the Kalb-Ramond field in string theory, and its nonabelian generalizations. It is desirable to discretize such `higher gauge theories' in a way analogous to lattice gauge theory, but with the fundamental geometric structures in the discretization boosted in dimension. As a step toward studying discrete versions of more general higher gauge theories, we consider the case of p-form electromagnetism. We show that discrete p-form electromagnetism admits a simple algebraic description in terms of chain complexes of abelian groups. Moreover, the model allows discrete spacetimes with quite general geometry, in contrast to the regular cubical lattices usually associated with lattice gauge theory. After constructing a suitable model of discrete spacetime for p-form electromagnetism, we quantize the theory using the Euclidean path integral formalism. The main result is a description of p-form electromagnetism as a `chain field theory' -- a theory analogous to topological quantum field theory, but with chain complexes replacing manifolds. This, in particular, gives a notion of time evolution from one `spacelike slice' of discrete spacetime to another.

Derek K. Wise

2005-10-08

352

Lattice formulations of supersymmetric gauge theories with matter fields

Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact lattice supersymmetry. Great ideas such as topological field theories, Dirac-Kaehler fermions, geometric discretization all come together to create supersymmetric lattice theories that are gauge-invariant, doubler free, local and exact supersymmetric. We discuss the recent lattice constructions of supersymmetric Yang-Mills theories in two and three dimensions coupled to matter fields in various representations of the color group.

Joseph, Anosh

2014-01-01

353

Six-dimensional unified field theory

The six-dimensional EM field equations with monopoles formulated by Teli and Palaskar (1984) and Teli (1984) are extended by analogy to encompass the gravitational, Heavisidian, strong, Proca, and weak fields, as well as the weak-field partner field proposed by Singh (1981). Six-dimensional gravito-Heavisidian field equations which are reducible to the standard four-dimensional forms are derived; complex electrogravitational and magneto-Heavisidian fields

M. T. Teli

1985-01-01

354

Deformations of Quantum Field Theories and Integrable Models

NASA Astrophysics Data System (ADS)

Deformations of quantum field theories which preserve Poincaré covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an infinite class of explicit examples is constructed on the Borchers-Uhlmann algebra underlying Wightman quantum field theory. These deformations exist independently of the space-time dimension, and contain the recently studied warped convolution deformation as a special case. In the special case of two-dimensional Minkowski space, they can be used to deform free field theories to integrable models with non-trivial S-matrix.

Lechner, Gandalf

2012-05-01

355

Quantum effective field theory of strongly correlated electron systems

A new theory, namely quantum effective-field theory of Fermion systems is proposed and it is applied to the Hubbard model for studying phase transitions. The key idea is to introduce an apparently gauge-breaking effective field and to apply it to the boundary of a cluster. This makes possible the exchange or transfer of electrons or holes between the inside and

Masuo Suzuki

1995-01-01

356

Relativistic field theory of neutron stars and their hyperon populations

The nuclear many-body problem is examined by means of the formulation of an effective relativistic field theory of interacting hadrons. A relativistic field theory of hadronic matter is especially appropriate for the description of hot or dense matter, because of the appearance of antiparticles and higher baryon resonances and because it automatically respects causality. 8 refs., 7 figs., 1 tab. (WRF)

Glendenning, N.K.

1986-01-01

357

Bose-Einstein Condensation of Atoms and Thermal Field Theory

The Bose-Einstein condensation of atoms can be conveniently formulated as a problem in thermal quantum field theory. There are many properties of the equilibrium system and its collective excitations that can be studied experimentally. The remarkable experimental control over all aspects of the system make it an ideal testing ground for the methods of thermal field theory.

Eric Braaten

1998-09-15

358

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed.

Jaekel, Christian D. [School of Mathematics, Cardiff University, Wales CF24 4AG (United Kingdom); Wreszinski, Walter F. [Departamento de Fisica Matematica, Instituto de Fisica, USP, Caixa Postal 66318, 05314-970 Sao Paulo (Brazil)

2011-01-15

359

Mean field theory for Heisenberg spin glasses G. Toulouse

L-103 Mean field theory for Heisenberg spin glasses G. Toulouse Laboratoire de Physique de l transitions sont prÃ©sentÃ©s. Abstract. 2014 The infinite-ranged spin glass model is studied in the general case. Kirkpatrick (SK), appears presently as the best definition of what mean field theory means for spin glasses

Boyer, Edmond

360

Neutrino and scalar boson mass in algebraic quantum field theory

The hypothesis is explored that fermion rest mass is due entirely to self-interaction via virtual excitation of gauge bosons. This requires revising the standard model to treat both chiral projections of a fermion field as SU(2) doublets, which precludes Yukawa coupling to a scalar (Higgs) boson field. The estimated self-interaction mass of the electron neutrino is $0.291\\times10^{-5}m_e$. The implied self-interaction mass of the Higgs boson itself is very small, comparable to the neutrino. Because there is no direct coupling to fermions, only to the $Z^0$ gauge boson, this can be reconciled with failure to detect low-mass Higgs bosons. This argument eliminates many undetermined parameters of the standard model, but requires an {\\it ad hoc} Lagrangian term to account for neutral current asymmetries. The proposed algebraic formalism is consistent with fermion generations defined by distinct eigenvalues of a self-interaction mass operator.

R. K. Nesbet

2007-11-08

361

NRQED Lagrangian at order 1/M4

NASA Astrophysics Data System (ADS)

The parity and time-reversal invariant effective Lagrangian for a heavy fermion interacting with an Abelian gauge field, i.e., NRQED, is constructed through order 1/M4. The implementation of Lorentz invariance in the effective theory becomes nontrivial at this order, and a complete solution for Wilson coefficient constraints is obtained. Matching conditions in the one-fermion sector are presented in terms of form factors and two-photon matrix elements of the nucleon. The extension of NRQED to describe interactions of the heavy fermion with a light fermion is introduced. Sample applications are discussed; these include the computation of nuclear structure effects in atomic bound states, the model-independent analysis of radiative corrections to low-energy lepton-nucleon scattering, and the study of static electromagnetic properties of nucleons.

Hill, Richard J.; Lee, Gabriel; Paz, Gil; Solon, Mikhail P.

2013-03-01

362

Topological field theory interpretations and LG representation of c = 1 string theory

NASA Astrophysics Data System (ADS)

We analyze the topological nature of c = 1 string theory at the self-dual radius. We find that it admits two distinct topological field theory structures characterized by two different puncture operators. We show it first in the unperturbed theory in which the only parameter is the cosmological constant, then in the presence of any infinitesimal tachyonic perturbation. We also discuss in detail a Landau-Ginzburg representation of one of the two topological field theory structures.

Bonora, L.; Xiong, C. S.

1995-02-01

363

GravitoMagnetic Field in Tensor-Vector-Scalar Theory

We study the gravitomagnetism in the TeVeS theory. We compute the gravitomagnetic field that a slow moving mass distribution produces in its Newtonian regime. We report that the consistency between the TeVeS gravitomagnetic field and that predicted by the Einstein-Hilbert theory leads to a relation between the vector and scalar coupling constants of the theory. We translate the Lunar Laser Ranging measurement's data into a constraint on the deviation from this relation.

Exirifard, Qasem, E-mail: exir@theory.ipm.ac.ir [Institute for Research in Fundamental Sciences (IPM), Tehran (Iran, Islamic Republic of)

2013-04-01

364

Effective field theory of resonant 2-level atoms

The phenomenological two-level atom is re-analysed using the methods of effective field theory. By presenting the Dicke-Jaynes-Cummings model in real space, an exact diagonalization is accomplished going beyond the rotating wave approximation. The meaning of the symmetries and conserved quantities in the theory is discussed and the model is related to non-equilibrium field theory. The structure of the solution raises a question about the rotating wave approximation in quantum mechanics.

Mark Burgess

1998-06-17

365

Non-commutative quantum geometric data in group field theories

We review briefly the motivations for introducing additional group-theoretic data in tensor models, leading to the richer framework of group field theories, themselves a field theory formulation of loop quantum gravity. We discuss how these data give to the GFT amplitudes the structure of lattice gauge theories and simplicial gravity path integrals, and make their quantum geometry manifest. We focus in particular on the non-commutative flux/algebra representation of these models.

Daniele Oriti

2014-05-08

366

Effective field theory: A modern approach to anomalous couplings

We advocate an effective field theory approach to anomalous couplings. The effective field theory approach is the natural way to extend the standard model such that the gauge symmetries are respected. It is general enough to capture any physics beyond the standard model, yet also provides guidance as to the most likely place to see the effects of new physics. The effective field theory approach also clarifies that one need not be concerned with the violation of unitarity in scattering processes at high energy. We apply these ideas to pair production of electroweak vector bosons. -- Highlights: •We discuss the advantages of effective field theories compared to anomalous couplings. •We show that one need not be concerned with unitarity violation at high energy. •We discuss the application of effective field theory to weak boson physics.

Degrande, Céline, E-mail: cdegrand@illinois.edu [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States) [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States); Centre for Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium); Greiner, Nicolas [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States) [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States); Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München (Germany); Kilian, Wolfgang [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States) [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States); University of Siegen, Fachbereich Physik, D-57068 Siegen (Germany); Mattelaer, Olivier [Centre for Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium)] [Centre for Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium); Mebane, Harrison; Stelzer, Tim; Willenbrock, Scott [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States)] [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States); Zhang, Cen [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States) [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States); Centre for Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium)

2013-08-15

367

Lorentz Violation in Supersymmetric Field Theories

Broken spacetime symmetries might emerge from a fundamental physical theory. The effective low-energy theory might be expected to exhibit violations of supersymmetry and Lorentz invariance. Some illustrative models which combine supersymmetry and Lorentz violation are described, and a superspace formulation is given.

M. S. Berger

2004-12-22

368

An Algebraic Approach to Quantum Field Theory

It is shown that two quantum theories dealing, respectively, in the Hilbert spaces of state vectors H1 and H2 are physically equivalent whenever we have a faithful representation of the same abstract algebra of observables in both spaces, no matter whether the representations are unitarily equivalent or not. This allows a purely algebraic formulation of the theory. The framework of

Rudolf Haag; Daniel Kastler

1964-01-01

369

Composite Fermion Wavefunctions Derived by Conformal Field Theory

The Jain theory of hierarchical Hall states is reconsidered in the light of recent analyses that have found exact relations between projected Jain wavefunctions and conformal field theory correlators. We show that the underlying conformal theory is precisely given by the W-infinity minimal models introduced earlier. This theory involves a reduction of the multicomponent Abelian theory that is similar to the projection to the lowest Landau level in the Jain approach. The projection yields quasihole excitations obeying non-Abelian fractional statistics. The analysis closely parallels the bosonic conformal theory description of the Pfaffian and Read-Rezayi states.

Andrea Cappelli

2012-06-30

370

Comparisons and connections between mean field dynamo theory and accretion disc theory

NASA Astrophysics Data System (ADS)

The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi-analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha-accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory.

Blackman, E. G.

2010-01-01

371

Pilot-wave approaches to quantum field theory

The purpose of this paper is to present an overview of recent work on pilot-wave approaches to quantum field theory. In such approaches, systems are not only described by their wave function, as in standard quantum theory, but also by some additional variables. In the non-relativistic pilot-wave theory of de Broglie and Bohm those variables are particle positions. In the context of quantum field theory, there are two natural choices, namely particle positions and fields. The incorporation of those variables makes it possible to provide an objective description of nature in which rather ambiguous notions such as `measurement' and `observer' play no fundamental role. As such, the theory is free of the conceptual difficulties, such as the measurement problem, that plague standard quantum theory.

Ward Struyve

2011-01-30

372

Atomic parity nonconservation, neutron radii, and effective field theories of nuclei

Accurately calibrated effective field theories are used to compute atomic parity nonconserving (APNC) observables. Although accurately calibrated, these effective field theories predict a large spread in the neutron skin of heavy nuclei. Whereas the neutron skin is strongly correlated to numerous physical observables, in this contribution we focus on its impact on new physics through APNC observables. The addition of an isoscalar-isovector coupling constant to the effective Lagrangian generates a wide range of values for the neutron skin of heavy nuclei without compromising the success of the model in reproducing well-constrained nuclear observables. Earlier studies have suggested that the use of isotopic ratios of APNC observables may eliminate their sensitivity to atomic structure. This leaves nuclear structure uncertainties as the main impediment for identifying physics beyond the standard model. We establish that uncertainties in the neutron skin of heavy nuclei are at present too large to measure isotopic ratios to better than the 0.1% accuracy required to test the standard model. However, we argue that such uncertainties will be significantly reduced by the upcoming measurement of the neutron radius in {sup 208}Pb at the Jefferson Laboratory.

Sil, Tapas; Centelles, M.; Vinas, X.; Piekarewicz, J. [Departament d'Estructura i Constituents de la Materia, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona (Spain); Department of Physics, Florida State University, Tallahassee, Florida 32306 (United States)

2005-04-01

373

Testing symmetries in effective models of higher derivative field theories

Higher derivative field theories with interactions raise serious doubts about their validity due to severe energy instabilities. In many cases the implementation of a direct perturbation treatment to excise the dangerous negative-energies from a higher derivative field theory may lead to violations of Lorentz and other symmetries. In this work we study a perturbative formulation for higher derivative field theories that allows the construction of a low-energy effective field theory being a genuine perturbations over the ordinary-derivative theory and having a positive-defined Hamiltonian. We show that some discrete symmetries are recovered in the low-energy effective theory when the perturbative method to reduce the negative-energy degrees of freedom from the higher derivative theory is applied. In particular, we focus on the higher derivative Maxwell-Chern-Simons model which is a Lorentz invariant and parity-odd theory in 2+1 dimensions. The parity violation arises in the effective action of QED{sub 3} as a quantum correction from the massive fermionic sector. We obtain the effective field theory which remains Lorentz invariant, but parity invariant to the order considered in the perturbative expansion.

Reyes, C. Marat [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, 04510 Mexico D.F. (Mexico)

2009-11-15

374

THE THEORY OF QUANTIZED FIELDS. II

The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the

J. Schwinger

1951-01-01

375

String field theory and tachyon dynamics

In this thesis we present some works done during my doctoral studies. These results focus on two directions. The first one is motivated by tachyon dynamics in open string theory. We calculate the stress tensors for the ...

Yang, Haitang, Ph. D. Massachusetts Institute of Technology

2006-01-01

376

Mean Field Theory for Sigmoid Belief Networks

We develop a mean eld theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean eld theory provides a tractable approximation to the true probability dis-tribution in these networks; it also yields a lower bound on the likelihood of evidence. We demon-strate the utility of this framework on a benchmark problem in statistical pattern recognition|the classi cation

Lawrence K. Saul; Tommi Jaakkola; Michael I. Jordan

1996-01-01

377

Quantum Hall Physics Equals Noncommutative Field Theory

In this note, we study a matrix-regularized version of non-commutative U(1) Chern- Simons theory proposed recently by Polychronakos. We determine a complete minimal basis of exact wavefunctions for the theory at arbitrary level k and rank N and show that these are in one-to-one correspondence with Laughlin-type wavefunctions describing excitations of a quantum Hall droplet composed of N electrons at

Simeon Hellerman; Mark Van Raamsdonk

378

Quantum field theory and the Jones polynomial

It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS3 to arbitrary three manifolds, giving invariants of three manifolds that are computable

Edward Witten

1989-01-01

379

NASA Astrophysics Data System (ADS)

We review a system of autonomous differential equations developed in our previous work [1] describing a flat cosmology filled with a barotropic fluid and a scalar field with a modified kinetic term of the form Script L = F(X) - V(?). We analyze the critical points and summarize the conditions to obtain scaling solutions. We consider a set of transformations and show that they leave invariant the equations of motion for the systems in which the scaling solution is obtained, allowing to reduce the number of degrees of freedom.

De-Santiago, Josue; Cervantes-Cota, Jorge L.

2014-03-01

380

The Lagrangian for mass dimension one fermions

The mass dimension one fermionic field associated with Elko satisfies the Klein-Gordon but not the Dirac equation. However, its propagator is not a Green's function of the Klein-Gordon operator. We determine the operator in which the associated Green's function is the propagator of the fermionic field. The field is still of mass dimension one, but the obtained Lagrangian resolves the last outstanding issue of mass dimension one fields. This Lagrangian does not admit local gauge invariance. Therefore, the mass dimension one fermions have limited interactions with the Standard Model particles and are natural dark matter candidates.

Cheng-Yang Lee

2014-04-21

381

Ghost Structure and Closed Strings in Vacuum String Field Theory

We complete the construction of vacuum string field theory by proposing a canonical choice of ghost kinetic term -- a local insertion of the ghost field at the string midpoint with an infinite normalization. This choice, supported by level expansion studies in the Siegel gauge, allows a simple analytic treatment of the ghost sector of the string field equations. As

Davide Gaiotto; Leonardo Rastelli; Ashoke Sen; Barton Zwiebach

2001-01-01

382

Some exact results on tachyon condensation in string field theory

The study of open string tachyon condensation in string field theory can be drastically simplified by making an appropriate choice of coordinates on the space of string fields. We show that a very natural coordinate system is suggested by the connection between the worldsheet renormalization group and spacetime physics. In this system only one field, the tachyon, condenses while all

David Kutasov; Marcos Mariño; Gregory Moore

2000-01-01

383

Tall tales from de Sitter space II: Field theory dualities

We consider the evolution of massive scalar fields in (asymptotically) de Sitter spacetimes of arbitrary dimension. Through the proposed dS\\/CFT correspondence, our analysis points to the existence of new nonlocal dualities for the Euclidean conformal field theory. A massless conformally coupled scalar field provides an example where the analysis is easily explicitly extended to 'tall' background spacetimes.

Frédéric Leblond; Robert C. Myers

2003-01-01

384

Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems

The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher-order field theories. However, a complete generalization to higher-order mechanical systems has yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher-order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.

Pedro D. Prieto-Martínez; Narciso Román-Roy

2011-06-16

385

This chapter presents a set of principles for the use of Grounded Theory techniques in qualitative field studies. Some issues and controversies relating to rigor in Grounded Theory generation are discussed. These include: inductive theory generation and emergence, how theoretical saturation may be judged, the extent to which coding schemes should be formalized, the objectivist- subjectivist debate, and the assessment

Susan Gasson

386

Renormalization of light-front Hamiltonian field theory

We propose a regularization of light-front field theory which does not make a distinction between transverse and longitudinal coordinates. It consists of a subtraction of low order terms in the Taylor expansion of an amplitude with respect to external momenta, similar to the regularization in the BPHZ scheme, which has some advantages that do not exist in covariant field theory. Instantaneous parts and oher longitudinal singularities are automatically removed irrespective of their explicit form. We argue therefore that these parts are meaningless. The local counterterms are equal to those of covariant field theory. We demonstrate the method in a number of examples, recovering the covariant results.

Ligterink, N.E.; Bakker, B.L.G. [Department of Physics and Astronomy, Vrije Universiteit, Amsterdam (Netherlands)] [Department of Physics and Astronomy, Vrije Universiteit, Amsterdam (Netherlands)

1995-11-15

387

Field Theory Model of the Flyby Anomaly

Precision tracking of spacecraft on interplanetary missions has turned up several anomalous deviations from predictions of general relativity. The Flyby Anomaly, wherein spacecraft gain or lose energy in an earth-centric frame after an encounter with earth, is clearly associated with the rotation of the earth. The possibility that the missing ingredient is a new type of potential field surrounding the earth is assessed in this write-up. A scalar field with the kinetic energy distribution of the earth as a source is evaluated numerically, with an amplitude parameter adjusted to match the data of Anderson et al.(2008). The new field can be interpreted as a coupling between kinetic energies of objects, a field analogous to fluid mechanics, or a field coupled to acceleration. The potential field violates various aspects of standard physics, such as energy non-conservation.

Lewis, R. A

2009-03-16

388

Spinor fields in Causal Set Theory

The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus additional scalar fields. Grassmann nature is being enforced by allowing measure to take both positive and negative values, and also by introducing a vector space to have both commutting dot product and anticommutting wedge product.

Roman Sverdlov

2008-08-21

389

Splitting fields and general differential Galois theory

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions. Bibliography: 14 titles.

Trushin, Dmitry V [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2010-11-11

390

Effective Lagrangian for Nonrelativistic Systems

NASA Astrophysics Data System (ADS)

The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing 1 dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in 1+1 dimensions.

Watanabe, Haruki; Murayama, Hitoshi

2014-07-01

391

Astrophysical magnetic fields and nonlinear dynamo theory

The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak ‘seed’ magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed

Axel Brandenburg; Kandaswamy Subramanian

2005-01-01

392

New class of effective field theories from embedded branes.

We present a new general class of four-dimensional effective field theories with interesting global symmetry groups. These theories arise from purely gravitational actions for (3+1)-dimensional branes embedded in higher dimensional spaces with induced gravity terms. The simplest example is the well known Galileon theory, with its associated Galilean symmetry, arising as the limit of a DGP brane world. However, we demonstrate that this is a special case of a much wider range of theories, with varying structures, but with the same attractive features such as second order equations. In some circumstances, these new effective field theories allow potentials for the scalar fields on curved space, with small masses protected by nonlinear symmetries. Such models may prove relevant to the cosmology of both the early and late universe. PMID:21770494

Goon, Garrett L; Hinterbichler, Kurt; Trodden, Mark

2011-06-10

393

Topological Field Theory of Time-Reversal Invariant Insulators

We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.

Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.

2010-03-19

394

Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.

We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics. PMID:12779582

Holm, Darryl D.

2002-06-01

395

A New Lorentz Violating Nonlocal Field Theory From String-Theory

A four-dimensional field theory with a qualitatively new type of nonlocality is constructed from a setting where Kaluza-Klein particles probe toroidally compactified string theory with twisted boundary conditions. In this theory fundamental particles are not pointlike and occupy a volume proportional to their R-charge. The theory breaks Lorentz invariance but appears to preserve spatial rotations. At low energies, it is approximately N=4 Super Yang-Mills theory, deformed by an operator of dimension seven. The dispersion relation of massless modes in vacuum is unchanged, but under certain conditions in this theory, particles can travel at superluminal velocities.

Ganor, Ori J.

2007-10-04

396

Theory of plasma confinement in non-axisymmetric magnetic fields.

The theory of plasma confinement by non-axisymmetric magnetic fields is reviewed. Such fields are used to confine fusion plasmas in stellarators, where in contrast to tokamaks and reversed-field pinches the magnetic field generally does not possess any continuous symmetry. The discussion is focussed on magnetohydrodynamic equilibrium conditions, collisionless particle orbits, and the kinetic theory of equilbrium and transport. Each of these topics is fundamentally affected by the absence of symmetry in the magnetic field: the field lines need not trace out nested flux surfaces, the particle orbits may not be confined, and the cross-field transport can be very large. Nevertheless, by tailoring the magnetic field appropriately, well-behaved equilibria with good confinement can be constructed, potentially offering an attractive route to magnetic fusion. In this article, the mathematical apparatus to describe stellarator plasmas is developed from first principles and basic elements underlying confinement optimization are introduced. PMID:25047050

Helander, Per

2014-08-01

397

Lagrangian Simulation of Combustion

A Lagrangian approach for the simulation of reactive flows has been developed during the course of this project, and has been applied to a number of significant and challenging problems including the transverse jet simulations. An efficient strategy for parallel domain decomposition has also been developed to enable the implementation of the approach on massively parallel architecture. Since 2005, we focused our efforts on the development of a semi-Lagrangian treatment of diffusion, and fast and accurate Lagrangian simulation tools for multiphysics problems including combustion.

Ahmed F. Ghoniem

2008-05-01

398

Pseudodynamical evolution and path integral in quantum field theory

Using the notion of distribution on an infinite dimensional space defined in our previous paper, we give definition of a version of dynamical evolution in quantum field theory, motivated by heuristic formulas involving path integrals.

A. V. Stoyanovsky

2008-10-27

399

Exceptional field theory. II. E[subscript 7(7)

We introduce the exceptional field theory for the group E[subscript 7(7)], based on a (4+56)-dimensional spacetime subject to a covariant section condition. The “internal” generalized diffeomorphisms of the coordinates in ...

Hohm, Olaf

400

Monopole solution in a Lorentz-violating field theory.

I present a topological defect solution that arises in a theory where Lorentz symmetry is spontaneously broken by a rank-two antisymmetric tensor field, and I discuss its observational signatures. PMID:21231216

Seifert, Michael D

2010-11-12

401

The Monte Carlo method in quantum field theory

This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo method with Markov-chain based importance sampling is presented. Properties of Markov chains are discussed in detail and several proofs are presented, culminating in the fundamental limit theorem for irreducible Markov chains. The example of a real scalar field theory is used to illustrate the Metropolis-Hastings method and to demonstrate the effectiveness of an action-preserving (microcanonical) local updating algorithm in reducing autocorrelations. The goal of these lectures is to provide the beginner with the basic skills needed to start carrying out Monte Carlo studies in quantum field theories, as well as to present the underlying theoretical foundations of the method.

Colin Morningstar

2007-02-20

402

Exactly stable collective oscillations in conformal field theory

Any conformal field theory (CFT) on a sphere supports completely undamped collective oscillations. We discuss the implications of this fact for studies of thermalization using AdS/CFT. Analogous oscillations occur in ...

Freivogel, Benjamin W.

403

Mutual information after a local quench in conformal field theory

We compute the entanglement entropy and mutual information for two disjoint intervals in two-dimensional conformal field theories as a function of time after a local quench, using the replica trick and boundary conformal field theory. We obtain explicit formulae for the universal contributions, which are leading in the regimes of, for example, close or well-separated intervals of fixed length. The results are largely consistent with the quasiparticle picture, in which entanglement above that present in the ground state is carried by pairs of entangled, freely propagating excitations. We also calculate the mutual information for two disjoint intervals in a proposed holographic local quench, whose holographic energy-momentum tensor matches the conformal field theory one. We find that the holographic mutual information shows qualitative differences from the conformal field theory results and we discuss possible interpretations of this.

Curtis T. Asplund; Alice Bernamonti

2013-11-17

404

Nuclear forces from chiral effective field theory: a primer

This paper is a write-up of introductory lectures on the modern approach to the nuclear force problem based on chiral effective field theory given at the 2009 Joliot-Curie School, Lacanau, France, 27 September - 3 October 2009.

Evgeny Epelbaum

2010-01-19

405

Nuclear forces from chiral effective field theory: a primer

This paper is a write-up of introductory lectures on the modern approach to the nuclear force problem based on chiral effective field theory given at the 2009 Joliot-Curie School, Lacanau, France, 27 September - 3 October 2009.

Epelbaum, Evgeny

2010-01-01

406

Quantum field theory in quantum set algebra

A modular quantum architecture is given for the space-time, particles, and fields of the Standard Model and General Relativity. It assumes a right-handed neutrino, so that based on their multiplet structure all fundamental fermions have isospin 1/2. This opens the possibility that the Higgs field can be identified with the Yang $i$-field of 1947. The quantum gravitational metric form proposed is a quantification of the Killing form of the quantum space-time cell. There is no trace of the black hole phenomenon at the one-cell quantum level.

David Ritz Finkelstein

2014-03-14

407

a Hierarchical Finite Element Method for Quantum Field Theory

NASA Astrophysics Data System (ADS)

We study a model of scalar quantum field theory (QFT) in which spacetime is a discrete set of points obtained by repeatedly subdividing a triangle into three triangles at the centroid. By integrating out the field variable at the centroid we get a renormalized action on the original triangle. The exact renormalization map between the angles of the triangles is obtained as well. The map can be used to find the partition function in scalar field theories in a recursive manner. A fixed point of this map is the cotangent formula in Finite Element Method which is used to find the energy stored in fields on a plane due to a Laplacian.

Kar, Arnab; Moolekamp, Fred; Rajeev, S. G.

2013-10-01

408

Field theories and exact stochastic equations for interacting particle systems

NASA Astrophysics Data System (ADS)

We consider the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further the issue of the “imaginary” Langevin noise that appears in the context of reaction-diffusion processes. Our procedure applies to a wide class of problems and is related to large deviation functional techniques developed recently to describe fluctuations of nonequilibrium systems in the hydrodynamic limit.

Andreanov, Alexei; Biroli, Giulio; Bouchaud, Jean-Philippe; Lefèvre, Alexandre

2006-09-01

409

Field theories and exact stochastic equations for interacting particle systems.

We consider the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further the issue of the "imaginary" Langevin noise that appears in the context of reaction-diffusion processes. Our procedure applies to a wide class of problems and is related to large deviation functional techniques developed recently to describe fluctuations of nonequilibrium systems in the hydrodynamic limit. PMID:17025576

Andreanov, Alexei; Biroli, Giulio; Bouchaud, Jean-Philippe; Lefèvre, Alexandre

2006-09-01

410

Quantum field theory cannot provide faster-than-light communication

We spell out a demonstration that, within the framework of quantum field theory, no faster-than-light communication can be established between observers. The steps of the demonstration are detailed enough to pinpoint which properties of the theory have been misinterpreted in previous papers claiming the existence of effects that could permit such communication. The developments described here can also be used

Phillippe H. Eberhard; Ronald R. Ross

1989-01-01

411

Thermodynamics and Finite size scaling in Scalar Field Theory

Thermodynamics and Finite size scaling in Scalar Field Theory A thesis submitted to the Tata Research, Mumbai December 2008 #12;ii #12;Synopsis In this work we study the thermodynamics of an interacting 4 theory in 4 space- time dimensions. The expressions for the thermodynamic quantities are worked

412

Relative motives and the theory of pseudo-finite fields

We generalize the motivic incarnation morphism from the theory of arithmetic integration to the relative case, where we work over a base variety S over a field k of characteristic zero. We develop a theory of constructible effective Chow motives over S, and we show how to associate a motive to any S-variety. We give a geometric proof of relative

Johannes Nicaise

2004-01-01

413

The Large N Limit of Superconformal Field Theories and Supergravity

We show that the large $N$ limit of certain conformal field theories in\\u000avarious dimensions include in their Hilbert space a sector describing\\u000asupergravity on the product of Anti-deSitter spacetimes, spheres and other\\u000acompact manifolds. This is shown by taking some branes in the full M\\/string\\u000atheory and then taking a low energy limit where the field theory on the

Juan M. Maldacena

1997-01-01

414

Non-commutative geometry and string field theory

An attempt is made to interpret the interactions of bosonic open strings as defining a non-cummulative, associative algebra, and to formulate the classical non-linear field theory of such strings in the language of non-commulative geometry. The point of departure is the BRST approach to string field theory. A setting is given in which there is a unique gauge invariant action,

Edward Witten

1986-01-01

415

Topological Graph Polynomials in Colored Group Field Theory

In this paper we analyze the open Feynman graphs of the Colored Group Field Theory introduced in [arXiv:0907.2582]. We define the boundary graph $\\cG_{\\partial}$ of an open graph $\\cG$ and prove it is a cellular complex. Using this structure we generalize the topological (Bollobas-Riordan) Tutte polynomials associated to (ribbon) graphs to topological polynomials adapted to Colored Group Field Theory graphs in arbitrary dimension.

Razvan Gurau

2009-11-10

416

Gas of wormholes in Euclidean quantum field theory

We model the spacetime foam picture by a gas of wormholes in Euclidean field theory. It is shown that at large distances the presence of such a gas leads merely to a renormalization of mass and charge values. We also demonstrate that there exist a class of specific distributions of point-like wormholes which essentially change the ultraviolet behavior of Green functions and lead to finite quantum field theories.

Savelova, E P

2012-01-01

417

Central charge bounds in 4D conformal field theory

We derive model-independent lower bounds on the stress tensor central charge C{sub T} in terms of the operator content of a 4-dimensional conformal field theory. More precisely, C{sub T} is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition.

Rattazzi, Riccardo; Vichi, Alessandro [Institut de Theorie des Phenomenes Physiques, EPFL, CH-1015 Lausanne (Switzerland); Rychkov, Slava [Laboratoire de Physique Theorique, Ecole Normale Superieure, and Faculte de Physique, Universite Pierre et Marie Curie (France)

2011-02-15

418

Algebraic solutions in Open String Field Theory - a lightning review

In this short talk we review basic ideas of string field theory with the emphasis on the recent developments. We show how without too much technicality one can look for analytic solutions to Witten's open string field theory. This is an expanded version of a talk given by the author over the last year at a number of occasions and notably at the conference "Selected Topics in Mathematical and Particle Physics" in honor of Prof. Jiri Niederle's 70th birthday.

Martin Schnabl

2010-04-27

419

Algebraic solutions in Open String Field Theory - a lightning review

In this short talk we review basic ideas of string field theory with the emphasis on the recent developments. We show how without much technicalities one could look for analytic solutions to Witten's open string field theory. This is an expanded version of a talk given by the author over the last year at number of occasions and notably at the conference "Selected Topics in Mathematical and Particle Physics" in honor of Prof. Jiri Niederle 70th birthday.

Schnabl, Martin

2010-01-01

420

Time Evolution in String Field Theory and T-duality

The time evolution operator (Schr\\"odinger functional) of quantum field theory can be expressed in terms of first quantised particles moving on the orbifold $S^1/Z_2$. We give a graphical derivation of this that generalises to second quantised string theory. T-duality then relates evolution through time t with evolution through 1/t and an interchange of string fields and backgrounds.

Anton Ilderton; Paul Mansfield

2004-10-27

421

The Gravitational Behaviour of an Effective Topological Field Theory

Effective topological field theories describe the topological properties of Dirac fermions in the low-energy regime. In this work, we consider fermions coupled to a $SO(5)$ Cartan connection on suitable four-dimensional compact manifolds. We show that the corresponding effective topological field theory, suitably constrained on the basis of topological motivations, gives rise to a gravitational action with a cosmological constant and Barbero-Immirzi parameter which is compatible, at classical level, with the vacuum general relativity.

Giandomenico Palumbo

2014-01-08

422

Effective field theories of baryons and mesons, or, what do quarks do?

This thesis is an attempt to understand the properties of the protons, pions and other hadrons in terms of their fundamental building blocks. In the first chapter the author reviews several of the approaches that have already been developed. The Nambu-Jona-Lasinio model offers the classic example of a derivation of meson properties from a quark Lagrangian. The chiral quark model encodes much of the intuition acquired in recent decades. The author also discusses the non-linear sigma model, the Skyrme model, and the constituent quark model, which is one of the oldest and most successful models. In the constituent quark model, the constituent quark appears to be different from the current quark that appears in the fundamental QCD Lagrangian. Recently it was proposed that the constituent quark is a topological soliton. In chapter 2 the author investigates this soliton, calculating its mass, radius, magnetic moment, color magnetic moment, and spin structure function. Within the approximations used, the magnetic moments and spin structure function cannot simultaneously be made to agree with the constituent quark model. In chapter 3 the author uses a different plan of attack. Rather than trying to model the constituents of the baryon, he begins with an effective field theory of baryons and mesons, with couplings and masses that are simply determined phenomenologically. Meson loop corrections to baryon axial currents are then computed in the 1/N expansion. It is already known that the one-loop corrections are suppressed by a factor 1/N; here it is shown that the two-loop corrections are suppressed by 1/N{sup 2}. To leading order, these corrections are exactly the same as would be calculated in the constituent quark model. This method therefore offers a different approach to the constituent quark.

Keaton, G.L. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group

1995-06-26

423

Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory

I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.

H. Nikolic

2006-10-12

424

Non-commutative geometry and chiral perturbation lagrangian

Chiral perturbation lagrangian in the framework of non-commutative geometry is considered in full detail. It is found that the explicit symmetry breaking terms appear and some relations between the coupling constants of the theory come out naturally. The WZW term also turns up on the same footing as the other terms of the chiral lagrangian.

Alishahiha, M; Kaviani, K

1996-01-01

425

BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is a tall order for a single chapter, relying rather heavily on additional background knowledge (for example supersymmetry) that students will not have unless they have already studied these topics in some depth. At this point students will need to be content with either appreciating the results as presented or else going to the original source material. The last four chapters of the book deal with anomalies and instantons, and again the reader is led from the simple material to the complex in a straightforward manner. Students should be able to follow the discussion both quantitatively and qualitatively, and become well-versed in understanding the 'big picture' provided they work through the material. The discussion on vacuum decay near the end of the book is quite timely given recent developments in eternal inflations, cosmic bubbles, and the like. The book contains a nice appendix that introduces students to the elements of Lie groups and Lie algebras that are required to understand a number of the ideas presented in various places in the book. There is also a short appendix on index theorems that should at least given students a basic sense of how these methods are employed in the subject at hand. This book would make a useful textbook for a mid-level graduate course. Though a bit terse in places, all of the main elements are there, in terms of both concept and methodology. It would make a fine addition to the library of any theorist in high-energy physics, gravitation, or cosmology.

Mann, Robert

2013-02-01

426

Statistical field theories deformed within different calculi

NASA Astrophysics Data System (ADS)

Within the framework of basic-deformed and finite-difference calculi, as well as deformation procedures proposed by Tsallis, Abe, and Kaniadakis and generalized by Naudts, we develop field-theoretical schemes of statistically distributed fields. We construct a set of generating functionals and find their connection with corresponding correlators for basic-deformed, finite-difference, and Kaniadakis calculi. Moreover, we introduce pair of additive functionals, which expansions into deformed series yield both Green functions and their irreducible proper vertices. We find as well formal equations, governing by the generating functionals of systems which possess a symmetry with respect to a field variation and are subjected to an arbitrary constrain. Finally, we generalize field-theoretical schemes inherent in concrete calculi in the Naudts manner. From the physical point of view, we study dependences of both one-site partition function and variance of free fields on deformations. We show that within the basic-deformed statistics dependence of the specific partition function on deformation has in logarithmic axes symmetrical form with respect to maximum related to deformation absence; in case of the finite-difference statistics, the partition function takes non-deformed value; for the Kaniadakis statistics, curves of related dependences have convex symmetrical form at small curvatures of the effective action and concave form at large ones. We demonstrate that only moment of the second order of free fields takes non-zero values to be proportional to inverse curvature of effective action. In dependence of the deformation parameter, the free field variance has linearly arising form for the basic-deformed distribution and increases non-linearly rapidly in case of the finite-difference statistics; for more complicated case of the Kaniadakis distribution, related dependence has double-well form.

Olemskoi, A. I.; Borysov, S. S.; Shuda, I. A.

2010-09-01

427

Nonlocal Field Theories at Finite Temperature and Density

NASA Astrophysics Data System (ADS)

In this thesis we investigate nonlocal fields in physics at finite temperature and density. We first investigate the thermodynamic properties of a nonlocal tachyon motivated by the nonlocal structure in string field theory. We use previously developed perturbative methods for nonlocal fields to calculate the partition function and the equation of state in the high temperature limit. We find that in these models the tachyons undergo a second order phase transition. We compare our results with those of ordinary scalar field theory. We also calculate the one loop finite temperature effective potential. We then investigate a nolocally modified effective field theory for nuclear matter. We pay particular attention to the effect of the modification on the two-loop diagrams. We then compare to the conventional case. We find that while we do end up with a softer behavior in the loop contributions this leads to only a minor reduction in the magnitude of the coupling constants.

Reddy, Abraham Suibba

428

Conformal field theories with infinitely many conservation laws

Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th

Todorov, Ivan [Institut des Hautes Etudes Scientifiques F-91440, Bures-sur-Yvette (France)] [Institut des Hautes Etudes Scientifiques F-91440, Bures-sur-Yvette (France)

2013-02-15

429

The Hilbert Lagrangian and Isometric Embedding: Tetrad Formulation of Regge-Teitelboim Gravity

We discuss Exterior Differential Systems (EDS) for the vacuum gravitational field. These EDS are derived by varying the Hilbert-Einstein Lagrangian, given most elegantly as a Cartan 4-forrm calibrating 4-spaces embedded in ten flat dimensions. In particular we thus formulate with tetrad equations the Regge-Teitelboim dynamics "a la string" (R-T); it arises when variation of the 4-spaces gives the Euler-Lagrange equations of a multicontact field theory. We calculate the Cartan character table of this EDS, showing the field equations to be well posed with no gauge freedom. The Hilbert Lagrangian as usually varied over just the intrinsic curvature structure of a 4-space yields only a subset of this dynamics, viz., solutions satisfying additional conditions constraining them to be Ricci-flat. In the static spherically symmetric case we present a new tetrad embedding in flat six dimensions, which allows reduction of the R-T field equations to a quadrature; the Schwarzschild metric is a special case. As has previously been noted there may be a classical correspondence of R-T theory with the hidden dimensions of brane theory, and perhaps this extended general relativistic dynamics holds in extreme circumstances where it can be interpreted as including a sort of dark or bulk energy, even though no term with a cosmological constant is included in the Lagrangian. As a multicontact system, canonical quantization should be straightforward.

Frank B. Estabrook

2009-08-03

430

Frame-like Lagrangians and presymplectic AKSZ-type sigma models

NASA Astrophysics Data System (ADS)

We study supergeometric structures underlying frame-like Lagrangians. We show that for the theory in n space-time dimensions both the frame-like Lagrangian and its gauge symmetries are encoded in the target supermanifold equipped with the odd vector field, the closed two-form of ghost degree n-1, and the scalar potential of ghost degree n. These structures satisfy a set of compatibility conditions ensuring the gauge invariance of the theory. The Lagrangian and the gauge symmetries have the same structures as those of AKSZ sigma model so that frame-like formulation can be seen as its presymplectic generalization. In contrast to the conventional AKSZ model, the generalization allows to describe systems with local degrees of freedom in terms of finite-dimensional target space. We argue that the proposed frame-like approach is directly related de Donder-Weyl polymomentum Hamiltonian formalism. Along with the standard field-theoretical examples like Einstein-Yang-Mills theory, we consider free higher spin fields, multi-frame gravity and parametrized systems. In particular, we propose the frame-like action for free totally symmetric massless fields that involves all higher spin connections on an equal footing.

Alkalaev, Konstantin; Grigoriev, Maxim

2014-07-01

431

NASA Astrophysics Data System (ADS)

Mineral dust aerosol is a key player in the Earth system. Strong winds over the world's major deserts mobilize and subsequently lift mineral dust high into the atmosphere. Due to the harshness and inaccessibility of desert regions, the exact processes of mobilisation and lifting, and layer formation are still unclear. One major unknown in the dust cycle is the dust source or emission strength. Despite better quantification being key for global models, the assessment of impacts on clouds, radiation and biogeochemical cycles, estimates in the literature from global and regional models span a wide range. Here, we employ the state-of-the-art Lagrangian particle dispersion model FLEXPART, which has been made capable of simulating dust mobilisation and settling, together with airborne and ground-based mineral aerosol and turbulence measurements from the Fennec/LADUNEX field campaign, which was carried out over the western Sahara during June 2011 to investigate the dust mobilisation processes for a case where a large Mesoscale Convective System triggered dust emissions in northern Mali. In comparison to in-situ and remote-sensing data from an aircraft and the CALIOP LIDAR observations, the FLEXPART dust transport simulations represent the overall shape and temporal evolution of the dust plume very well. The reliability of ECMWF analysis data in the vicinity of a convectively-generated dust plume is assessed using a set of model simulations, in which dust emissions are prescribed manually from SEVIRI satellite images. Our results confirm that dust emission by small-scale processes associated with deep moist convection remain a key problem for reliable dust simulations. Overall, this research underlines the potential of jointly using measurements and observations from many data sources with models to better understand dust emission processes in the Sahara desert, and to thereby reduce model uncertainty.

Sodemann, H.; Lai, M.; Knippertz, P.; Bart, M.; Marenco, F.; McQuaid, J. B.; Rosenberg, P.; Ryder, C. L.

2012-12-01

432

The effective Lagrangian of dark energy from observations

NASA Astrophysics Data System (ADS)

Using observational data on the expansion rate of the universe (H(z)) we constrain the effective Lagrangian of the current accelerated expansion. Our results show that the effective potential is consistent with being flat i.e., a cosmological constant; it is also consistent with the field moving along an almost flat potential like a pseudo-Goldstone boson. We show that the potential of dark energy does not deviate from a constant at more than 6% over the redshift range 0 < z < 1. The data can be described by just a constant term in the Lagrangian and do not require any extra parameters; therefore there is no evidence for augmenting the number of parameters of the LCDM paradigm. We also find that the data justify the effective theory approach to describe accelerated expansion and that the allowed parameters range satisfy the expected hierarchy. Future data, both from cosmic chronometers and baryonic acoustic oscillations, that can measure H(z) at the % level, could greatly improve constraints on the flatness of the potential or shed some light on possible mechanisms driving the accelerated expansion. Besides the above result, it is shown that the effective Lagrangian of accelerated expansion can be constrained from cosmological observations in a model-independent way and that direct measurements of the expansion rate H(z) are most useful to do so.

Jimenez, Raul; Talavera, P.; Verde, Licia; Moresco, Michele; Cimatti, Andrea; Pozzetti, Lucia

2012-03-01

433

Rational SFT, linearized Legendrian contact homology, and Lagrangian Floer cohomology

We relate the version of rational Symplectic Field Theory for exact Lagrangian cobordisms introduced in [5] with linearized Legendrian contact homology. More precisely, if $L\\subset X$ is an exact Lagrangian submanifold of an exact symplectic manifold with convex end $\\Lambda\\subset Y$, where $Y$ is a contact manifold and $\\Lambda$ is a Legendrian submanifold, and if $L$ has empty concave end, then the linearized Legendrian contact cohomology of $\\Lambda$, linearized with respect to the augmentation induced by $L$, equals the rational SFT of $(X,L)$. Following ideas of P. Seidel, this equality in combination with a version of Lagrangian Floer cohomology of $L$ leads us to a conjectural exact sequence which in particular implies that if $X=\\C^{n}$ then the linearized Legendrian contact cohomology of $\\Lambda\\subset S^{2n-1}$ is isomorphic to the singular homology of $L$. We outline a proof of the conjecture and show how to interpret the duality exact sequence for linearized contact homology of [6] in terms of ...

Ekholm, Tobias

2009-01-01

434

Fundamental string solutions in open string field theories

NASA Astrophysics Data System (ADS)

In Witten’s open cubic bosonic string field theory and Berkovits’ superstring field theory we investigate solutions of the equations of motion with appropriate source terms, which correspond to Callan-Maldacena solution in Born-Infeld theory representing fundamental strings ending on the D-branes. The solutions are given in order by order manner, and we show some full order properties in the sense of ?' expansion. In superstring case we show that the solution is 1/2 BPS in full order.

Michishita, Yoji

2006-02-01

435

Torque anomaly in quantum field theory

NASA Astrophysics Data System (ADS)

The expectation values of energy density and pressure of a quantum field inside a wedge-shaped region appear to violate the expected relationship between torque and total energy as a function of angle. In particular, this is true of the well-known Deutsch-Candelas stress tensor for the electromagnetic field, whose definition requires no regularization except possibly at the vertex. Unlike a similar anomaly in the pressure exerted by a reflecting boundary against a perpendicular wall, this problem cannot be dismissed as an artifact of an ad hoc regularization.

Fulling, S. A.; Mera, F. D.; Trendafilova, C. S.

2013-02-01

436

Maxwell group and HS field theory

NASA Astrophysics Data System (ADS)

We consider the master fields for HS multiplets defined on 10-dimensional tensorial extension of D = 4 space-time described as a coset of 16-parameter Maxwell group . The tensorial coordinates provide a geometrization of the coupling to constant uniform EM fields. We describe the spinorial model in extended space-time and by its first quantization we obtain new infinite HS-Maxwell multiplets with their massless components coupled to each other through constant EM background. We conclude our report by observing that three-dimensional spinorial model with a pair of spinors should provide after quantization D = 3 massive HS-Maxwell multiplets.

Fedoruk, Sergey; Lukierski, Jerzy

2013-11-01

437

Field Theories of Condensed Matter Physics

NASA Astrophysics Data System (ADS)

1. Introduction; 2. The Hubbard model; 3. The magnetic instability of the Fermi system; 4. The renormalization group and scaling; 5. One-dimensional quantum antiferromagnets; 6. The Luttinger liquid; 7. Sigma models and topological terms; 8. Spin liquid states; 9. Gauge theory, dimer models, and topological phases; 10. Chiral spin states and anyons; 11. Anyon superconductivity; 12. Topology and quantum Hall effect; 13. The fractional quantum Hall effect; 14. Topological fluids; 15. Physics at the edge; 16. Topological insulators; 17. Quantum entanglement; References; Index.

Fradkin, Eduardo

2013-02-01

438

Nonlinear Dynamical Mean-Field Theory

is partially filled, so electrons can easily move. In insulators, the bands are completely filled, with a band-gap to the first unoccupied band. Â· The electrons move with an effective velocity v(k)=d(k)/dk. So they carry field creates a periodic ac current in a perfect metal with electrons moving in a crystalline lattice. J

Freericks, Jim

439

Logarithmic correlators in nonrelativistic conformal field theory

We show how logarithmic terms may arise in the correlators of fields which belong to the representation of the Schroedinger-Virasoro algebra or the affine Galilean conformal algebra (GCA). We show that in GCA, only scaling operator can have a Jordan form and rapidity cannot. We observe that in both algebras, logarithmic dependence appears along the time direction alone.

Hosseiny, Ali; Rouhani, Shahin [Department of Physics, Sharif University of Technology, Tehran 11165-9161 (Iran, Islamic Republic of)

2010-10-15

440

Novel collective excitations in a hot scalar field theory

We study the spectrum of quasiparticles in a scalar quantum field theory at high temperature. Our results indicate the existence of novel quasiparticles with purely collective origin at low momenta for some choices of the masses and coupling. Scalar fields play a prominent role in many models of cosmology, and their collective excitations could be relevant for transport phenomena in the early universe.

Marco Drewes

2013-11-26

441

221B Lecture Notes Quantum Field Theory II (Fermi Systems)

221B Lecture Notes Quantum Field Theory II (Fermi Systems) 1 Statistical Mechanics of Fermions 1- commutation relation and becomes Grassmann-odd number in the classical limit. Clearly, a Grassmann-odd classical Fermi field is not an observable as no measurement would yield a Grassmann-odd number as a result

Murayama, Hitoshi

442

221B Lecture Notes Quantum Field Theory III (Fermi Systems)

221B Lecture Notes Quantum Field Theory III (Fermi Systems) 1 Statistical Mechanics of Fermions 1- commutation relation and becomes Grassmann-odd number in the classical limit. Clearly, a Grassmann-odd classical Fermi field is not an observable as no measurement would yield a Grassmann-odd number as a result

Murayama, Hitoshi

443

Infinite conformal symmetry in two-dimensional quantum field theory

We present an mvestlgaUon of the massless, two-dimensional, interacting field theories Their basic property is their invanance under an lnfimte-dlmenslonal group of conformal (analytic) transformations It is shown that the local fields forlmng the operator algebra can be classified according to the irreducible representations of Vtrasoro algebra, and that the correlation functions are bmlt up of the \\

A A Belavin; A M Polyakov; A B Zamolodchikov

1984-01-01

444

SUSY gauge theory on graded manifolds

Lagrangian classical field theory of even and odd fields is adequately formulated in terms of fibre bundles and graded manifolds. In particular, conventional Yang-Mills gauge theory is theory of connections on smooth principal bundles, but its BRST extension involves odd ghost fields an antifields on graded manifolds. Here, we formulate Yang-Mills theory of Grassmann-graded gauge fields associated to Lie superalgebras on principal graded bundles. A problem lies in a geometric definition of odd gauge fields. Our goal is Yang--Mills theory of graded gauge fields and its BRST extension.

G. Sardanashvily; W. Wachowski

2014-06-24

445

Generalization of the theory of far-field caustics by the catastrophe theory.

To generalize the theory of far-field caustics, three theorems and several corollaries are presented in this paper. Using the law of reflection and catastrophe theory we have established conditions to predict caustic patterns in a 3-D space, which were created from the reflection of a light beam from an analytically known surface. The general theory was readily reduced to the already known cases of diffraction, indicating the validity of the general theory. Experimental evidence in two simple cases of reflectors, consisting of triangular and rectangular membranes, corroborated the results of the theory. PMID:20389809

Theocaris, P S; Michopoulos, J G

1982-03-15

446

The Potential-Vortex Theory of the Electromagnetic Field

Maxwell-Lorenz theory describes only vortex electromagnetic processes. Potential component of the magnetic field is usually excluded by the introduction of mathematical terms: Coulomb and Lorenz gauges. Proposed approach to the construction of the four-dimensional electrodynamics based on the total (four-dimensional) field theory takes into account both vortex and potential components of its characteristics. It is shown that potential components of the electromagnetic field have physical content. System of modified (generalized) Maxwell equations is written. With their help contradictions usually appearing while describing the distribution of electromagnetic waves, are eliminated. Works of other authors obtained similar results are presented and analyzed.

A. K. Tomilin

2010-08-24

447

On Rényi entropies of disjoint intervals in conformal field theory

NASA Astrophysics Data System (ADS)

We study the Rényi entropies of N disjoint intervals in the conformal field theories describing the free compactified boson and the Ising model. They are computed as the 2N-point function of twist fields, by employing the partition function of the model on a particular class of Riemann surfaces. The results are written in terms of Riemann theta functions. The prediction for the free boson in the decompactification regime is checked against exact results for the harmonic chain. For the Ising model, matrix product state computations agree with the conformal field theory result once the finite size corrections have been taken into account.

Coser, Andrea; Tagliacozzo, Luca; Tonni, Erik

2014-01-01

448

Cold atom simulation of interacting relativistic quantum field theories

We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.

J. Ignacio Cirac; Paolo Maraner; Jiannis K. Pachos

2010-06-15

449

Energy Inequalities in Quantum Field Theory

Quantum fields are known to violate all the pointwise energy conditions of classical general relativity. We review the subject of quantum energy inequalities: lower bounds satisfied by weighted averages of the stress-energy tensor, which may be regarded as the vestiges of the classical energy conditions after quantisation. Contact is also made with thermodynamics and related issues in quantum mechanics, where such inequalities find analogues in sharp Gaarding inequalities.

Christopher J. Fewster

2005-01-31

450

Dirac field theory in rotating coordinates

The Dirac field in Minkowski space-time is quantized in a rotating coordinate system. In contrast to the scalar case, the natural procedure of defining particles via the Killing vector of the rotating observer yields a canonical quantization scheme. This scheme is inequivalent to the usual Minkowski quantization, and in contrast to the scalar case the rotating observer sees in the inertial vacuum a (nonthermal) spectrum of particles and antiparticles.

Iyer, B.R.

1982-10-15

451

Light-front chiral effective field theory

We propose a general framework to calculate the nonperturbative structure of relativistic bound state systems. The state vector of the bound state is calculated in the covariant formulation of light-front dynamics. In this scheme, the state vector is defined on the light front of general position {omega} {center_dot} x = 0, where {omega} is an arbitrary light-like four-vector. This enables a strict control of any violation of rotational invariance. The state vector is then decomposed in Fock components. Our formalism is applied to the description of the nucleon properties at low energy, in chiral perturbation theory. We also show that the use of a recently proposed regularization scheme, the so-called Taylor-Lagrange regularization scheme, is very adequate in order to treat divergences in this nonperturbative framework.

Mathiot, J.-F. [Laboratoire de Physique Corpusculaire (France)] [Laboratoire de Physique Corpusculaire (France); Tsirova, N. A., E-mail: ntsirova@ssu.samara.ru [Samara State University (Russian Federation)

2013-11-15

452

Holographic thermal field theory on curved spacetimes

The AdS/CFT correspondence relates certain strongly coupled CFTs with large effective central charge $c_\\text{eff}$ to semi-classical gravitational theories with AdS asymptotics. We describe recent progress in understanding gravity duals for CFTs on non-trivial spacetimes at finite temperature, both in and out of equilibrium. Such gravity methods provide powerful new tools to access the physics of these strongly coupled theories, which often differs qualitatively from that found at weak coupling. Our discussion begins with basic aspects of AdS/CFT and progresses through thermal CFTs on the Einstein Static Universe and on periodically identified Minkowski spacetime. In the latter context we focus on states describing so-called plasma balls, which become stable at large $c_\\text{eff}$. We then proceed to out-of-equilibrium situations associated with dynamical bulk black holes. In particular, the non-compact nature of these bulk black holes allows stationary solutions with non-Killing horizons that describe time-independent flows of CFT plasma. As final a topic we consider CFTs on black hole spacetimes. This discussion provides insight into how the CFT transports heat between general heat sources and sinks of finite size. In certain phases the coupling to small sources can be strongly suppressed, resulting in negligible heat transport despite the presence of a deconfined plasma with sizeable thermal conductivity. We also present a new result, explaining how this so-called droplet behaviour is related to confinement via a change of conformal frame.

Donald Marolf; Mukund Rangamani; Toby Wiseman

2013-12-02

453

Linear approximation in the nonsymmetric Kaluza-Klein theory

NASA Astrophysics Data System (ADS)

The present investigation is concerned with the linear approximation of the nonsymmetric Kaluza-Klein theory reported by Kalinowski (1982, 1983). The elements of the nonsymmetric Kaluza-Klein theory are examined, taking into account the definition of a nonsymmetric metric tensor on the space-time E, the Lagrangian in the nonsymmetric Kaluza-Klein theory, and the Lagrangian in the gravitational field in the nonsymmetric theory of gravitation. Attention is given to the linearization of the nonsymmetric Kaluza-Klein theory (electromagnetic case, the linearization of the nonsymmetric-nonabelian Kaluza-Klein theory (general case), geodetic lines, and equations of motion for a test particle.

Mann, R. B.; Kalinowski, M. W.

1984-03-01

454

Quark Phase Transition Parameters and $?$-Meson Field in RMF Theory

The deconfinement phase transition from hadronic matter to quark matter in the interior of compact stars is investigated. The hadronic phase is described in the framework of relativistic mean-field (RMF) theory, when also the scalar- isovector $\\delta$-meson effective field is taken into account. To describe a quark phase the MIT bag model is used. The changes of the mixed phase threshold parameters caused by the presence of $\\delta$-meson field are investigated.

G. B. Alaverdyan

2009-07-23

455

Topics in Holography and Four Dimensional Superconformal Field Theories

NASA Astrophysics Data System (ADS)

Strong dynamics in physical systems underpin a plethora of phenomena in nature. However, there had not exist many theoretical tools for probing such systems in quantum field theories until the discovery of supersymmetry and holography. In this thesis, we use these frameworks to study strongly coupled dynamics. In chapters two and three, we compute the entanglement entropy of several field theories at zero and finite temperature by using a holographic proposal. We find that the scaling of the entanglement entropy as a function of the size of the system is different in the various phases of the theory. This indicates that the entanglement entropy can be used to detect phase transitions in field theories. For all the systems we studied, we use the entanglement entropy to characterise the types of transitions present. In chapters four and five, we find consistent truncations of the fermionic sectors of M-theory and JIB superstring theory compactified on Sasaki-Einstein seven and five manifolds, respectively. The goal in these chapters is to provide string theory and M-theory embeddings of phenomenological studies of condensed matter systems in holography. We were unable to find truncations to a single fermion as is required by many models. The truncations also contain new types of couplings that were not studied in the literature. Thus we also provided motivations for new phenomenological models. In chapter six, we develop methods for constructing strongly interacting

Bah, Ibrahima

456

A lagrangian dispersion model for calculating concentration distribution within a built-up domain

A Lagrangian model to study the dispersion of pollutants between urban buildings is described. The flow field is supplied by an objective analysis (Rockle (1990) Ph.D. thesis, Vom Fachbereich Mechanik, der Technischen Hochschule Darmstadt, Germany) and is adjusted to satisfy the continuity equation. From the resulting; mass consistent field the Lagrangian diffusion parameters are eliminated. A 3-D Lagrangian diffusion model

H. Kaplan; N. Dinar

1996-01-01

457

Warped Conformal Field Theory as Lower Spin Gravity

Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non AdS space-times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL(2,R) x U(1) Chern-Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non AdS geometries. This case represents the first step towards understanding a fully invariant formalism for W_N field theories and their holographic duals.

Diego M. Hofman; Blaise Rollier

2014-11-03

458

Quantum Mind from a Classical Field Theory of the Brain

We suggest that, with regard to a theory of quantum mind, brain processes can be described by a classical, dissipative, non-abelian gauge theory. In fact, such a theory has a hidden quantum nature due to its non-abelian character, which is revealed through dissipation, when the theory reduces to a quantum vacuum, where temperatures are of the order of absolute zero, and coherence of quantum states is preserved. We consider in particular the case of pure SU(2) gauge theory with a special anzatz for the gauge field, which breaks Lorentz invariance. In the ansatz, a contraction mapping plays the role of dissipation. In the limit of maximal dissipation, which corresponds to the attractive fixed point of the contraction mapping, the gauge fields reduce, up to constant factors, to the Pauli quantum gates for one-qubit states. Then tubuline-qubits can be processed in the quantum vacuum of the classical field theory of the brain, where decoherence is avoided due to the extremely low temperature. Finally, we interpret the classical SU(2) dissipative gauge theory as the quantum metalanguage (relative to the quantum logic of qubits), which holds the non-algorithmic aspect of the mind.

Paola Zizzi

2011-04-13

459

Historically it happen so that in branches of physics connected with field theory and of physics of material systems (continuous media) the concept of "conservation laws" has a different meaning. In field theory "conservation laws" are those that claim the existence of conservative physical quantities or objects. These are conservation laws for physical fields. In contrast to that in physics (and mechanics) of material systems the concept of "conservation laws" relates to conservation laws for energy, linear momentum, angular momentum, and mass that establish the balance between the change of physical quantities and external action. In the paper presented it is proved that there exist a connection between of conservation laws for physical fields and those for material systems. This points to the fact that physical fields are connected with material systems. Such results has an unique significance for field theories. This enables one to substantiate many basic principles of field theories, such as, for example, the unity of existing field theories and the causality. The specific feature of field theory equations, namely, their connection to the equations for material systems, is elicited. Such results have been obtained by using skew-symmetric differential forms, which reflect the properties of conservation laws.

L. I. Petrova

2008-12-02

460

String field theory solution for any open string background

NASA Astrophysics Data System (ADS)

We present an exact solution of open bosonic string field theory which can be used to describe any time-independent open string background. The solution generalizes an earlier construction of Kiermaier, Okawa, and Soler, and assumes the existence of boundary condition changing operators with nonsingular OPEs and vanishing conformal dimension. Our main observation is that boundary condition changing operators of this kind can describe nearly any open string background provided the background shift is accompanied by a timelike Wilson line of sufficient strength. As an application we analyze the tachyon lump describing the formation of a D$(p-1)$-brane in the string field theory of a D$p$-brane, for generic compactification radius. This not only provides a proof of Sen's second conjecture, but also gives explicit examples of higher energy solutions, confirming analytically that string field theory can "reverse" the direction of the worldsheet RG flow. We also find multiple D-brane solutions, demonstrating that string field theory can add Chan-Paton factors and change the rank of the gauge group. Finally, we show how the solution provides a remarkably simple and nonperturbative proof of the background independence of open bosonic string field theory.

Erler, Theodore; Maccaferri, Carlo

2014-10-01

461

Ph.D. Thesis: Quantum Field Theory and Gravity in Causal Sets

This is is a copy of dissertation that I have submitted in defense of my ph.d. thesis, with some minor changes that I have made since then. The goal of the project is to generalize matter fields and their Lagrangians from regular space time to causal sets.

Roman Sverdlov

2009-05-14

462

Ph.D. Thesis: Quantum Field Theory and Gravity in Causal Sets

NASA Astrophysics Data System (ADS)

This is is a copy of dissertation that I have submitted in defense of my ph.d. thesis, with some minor changes that I have made since then. The goal of the project is to generalize matter fields and their Lagrangians from regular space time to causal sets.

Sverdlov, Roman

2009-05-01

463

We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Ho?ava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit. PMID:23473127

Janiszewski, Stefan; Karch, Andreas

2013-02-22

464

Analytic approximations, perturbation theory, effective field theory methods and their applications

We summarize the parallel session B4: 'Analytic approximations, perturbation theory effective field theory methods and their applications' and the joint session B2/B4: 'Approximate solutions to Einstein equations: Methods and Applications', of the GR20 & Amaldi10 conference in Warsaw, July 2013. The contributed talks reported significant advances on various areas of research in gravity.

Vitor Cardoso; Rafael A. Porto

2014-01-09

465

Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory

An elementary field-theoretic mechanism is proposed that allows one\\u000aLagrangian to describe a family of particles having different masses but\\u000aotherwise similar physical properties. The mechanism relies on the observation\\u000athat the Dyson-Schwinger equations derived from a Lagrangian can have many\\u000adifferent but equally valid solutions. Nonunique solutions to the\\u000aDyson-Schwinger equations arise when the functional integral for the Green's

Carl M. Bender; S. P. Klevansky

2010-01-01

466

Localization and diffusion in polymer quantum field theory

Polymer quantization is a non-standard approach to quantizing a classical system inspired by background independent approaches to quantum gravity such as loop quantum gravity. When applied to field theory it introduces a characteristic polymer scale at the level of the fields classical configuration space. Compared with models with space-time discreteness or non-commutativity this is an alternative way in which a characteristic scale can be introduced in a field theoretic context. Motivated by this comparison we study here localization and diffusion properties associated with polymer field observables and dispersion relation in order to shed some light on the novel physical features introduced by polymer quantization. While localization processes seems to be only mildly affected by polymer effects, we find that polymer diffusion differs significantly from the "dimensional reduction" picture emerging in other Planck-scale models beyond local quantum field theory.

Michele Arzano; Marco Letizia

2014-08-13

467

Localization and diffusion in polymer quantum field theory

Polymer quantization is a non-standard approach to quantizing a classical system inspired by background independent approaches to quantum gravity such as loop quantum gravity. When applied to field theory it introduces a characteristic polymer scale at the level of the fields classical configuration space. Compared with models with space-time discreteness or non-commutativity this is an alternative way in which a characteristic scale can be introduced in a field theoretic context. Motivated by this comparison we study here localization and diffusion properties associated with polymer field observables and dispersion relation in order to shed some light on the novel physical features introduced by polymer quantization. While localization processes seems to be only mildly affected by polymer effects, we find that polymer diffusion differs significantly from the "dimensional reduction" picture emerging in other Planck-scale models beyond local quantum field theory.

Arzano, Michele

2014-01-01

468

Quantum field theories on algebraic curves. I. Additive bosons

NASA Astrophysics Data System (ADS)

Using Serre's adelic interpretation of cohomology, we develop a `differential and integral calculus' on an algebraic curve X over an algebraically closed field k of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on X and prove the corresponding generalized residue theorem. Using the representation theory of the global Heisenberg algebra and lattice Lie algebra, we formulate quantum field theories of additive and charged bosons on an algebraic curve X. These theories are naturally connected with the algebraic de Rham theorem. We prove that an extension of global symmetries (Witten's additive Ward identities) from the k-vector space of rational functions on X to the vector space of additive multi-valued functions uniquely determines these quantum theories of additive and charged bosons.

Takhtajan, Leon A.

2013-04-01

469

Predictiveness of Effective Field Theory in Nuclear Physics

We discuss the role effective field theory plays in making predictions in nuclear physics in an approach that combines both the high sophistication of the standard nuclear many-body approach and the power of systematic higher chiral-order account in chiral perturbation theory. The main idea of this approach is illustrated with a selected number of cases involving few-body systems, the measurement of some of which poses an experimental challenge and will be of value to solar neutrino studies.

Mannque Rho

2006-10-01

470

Consistent Kaluza-Klein Truncations via Exceptional Field Theory

We present the generalized Scherk-Schwarz reduction ansatz for the full supersymmetric exceptional field theory in terms of group valued twist matrices subject to consistency equations. With this ansatz the field equations precisely reduce to those of lower-dimensional gauged supergravity parametrized by an embedding tensor. We explicitly construct a family of twist matrices as solutions of the consistency equations. They induce gauged supergravities with gauge groups SO(p,q) and CSO(p,q,r). Geometrically, they describe compactifications on internal spaces given by spheres and (warped) hyperboloides $H^{p,q}$, thus extending the applicability of generalized Scherk-Schwarz reductions beyond homogeneous spaces. Together with the dictionary that relates exceptional field theory to D=11 and IIB supergravity, respectively, the construction defines an entire new family of consistent truncations of the original theories. These include not only compactifications on spheres of different dimensions (such as AdS$_5\\time...

Hohm, Olaf

2014-01-01

471

Comments on Entanglement Negativity in Holographic Field Theories

We explore entanglement negativity, a measure of the distillable entanglement contained in a quantum state, in relativistic field theories in various dimensions. We first give a general overview of negativity and its properties and then explain a well known result relating (logarithmic) negativity of pure quantum states to the Renyi entropy (at index $1/2$), by exploiting the simple features of entanglement in thermal states. In particular, we show that the negativity of the thermofield double state is given by the free energy difference of the system at temperature $T$ and $2\\,T$ respectively. We then use this result to compute the negativity in the vacuum state of conformal field theories in various dimensions, utilizing results that have been derived for free and holographic CFTs in the literature. We also comment upon general lessons to be learnt about negativity in holographic field theories.

Rangamani, Mukund

2014-01-01

472

Comments on Entanglement Negativity in Holographic Field Theories

We explore entanglement negativity, a measure of the distillable entanglement contained in a quantum state, in relativistic field theories in various dimensions. We first give a general overview of negativity and its properties and then explain a well known result relating (logarithmic) negativity of pure quantum states to the Renyi entropy (at index $1/2$), by exploiting the simple features of entanglement in thermal states. In particular, we show that the negativity of the thermofield double state is given by the free energy difference of the system at temperature $T$ and $2\\,T$ respectively. We then use this result to compute the negativity in the vacuum state of conformal field theories in various dimensions, utilizing results that have been derived for free and holographic CFTs in the literature. We also comment upon general lessons to be learnt about negativity in holographic field theories.

Mukund Rangamani; Massimiliano Rota

2014-06-26

473

A Hierarchy of Effective Field Theories of Hot Electroweak Matter

Abst\\-ract: A hierarchy of effective three-dimensional theories of finite temperature electroweak matter is studied. First an integration over non-static modes leads to an effective theory containing a gauge field $A_{i}^{a}$, an adjoint Higgs field $A_{0}^a$ and the fundamental Higgs field $\\phi_{\\alpha}$. We carry out the integration in the 1-loop approximation, study renormalisation effects and estimate quantitatively those terms of the effective action which are suppressed by inverse powers of the temperature. Secondly, because of the existence of well-separated thermal mass scales, $A_{0}^a$ can be integrated over, and finally also $\\phi_{\\alpha}$, leaving an effective theory of the $A_{i}^{a}$.In the analysis of the subsequent models particular attention is paid to the screening of the magnetic fluctuations due to the integrated-out degrees of freedom. Files of 2 Tables and 4 Figures are available in (la)tex-format upon request

A. Jakovác; K. Kajantie; A. Patkós

1993-12-30

474

Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes

NASA Astrophysics Data System (ADS)

The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to noncommutative gravity. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models. In part two we develop a new formalism for quantum field theory on noncommutative curved spacetimes by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. We also study explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories. The convergent deformation of simple toy models is investigated and it is found that these theories have an improved behaviour at short distances, i.e. in the ultraviolet. In part three we study homomorphisms between and connections on noncommutative vector bundles. We prove that all homomorphisms and connections of the deformed theory can be obtained by applying a quantization isomorphism to undeformed homomorphisms and connections. The extension of homomorphisms and connections to tensor products of bimodules is clarified. As a nontrivial application of the new mathematical formalism we extend our studies of exact noncommutative gravity solutions to more general deformations.

Schenkel, Alexander

2012-10-01

475

General Physics Motivations for Numerical Simulations of Quantum Field Theory

In this introductory article a brief description of Quantum Field Theories (QFT) is presented with emphasis on the distinction between strongly and weakly coupled theories. A case is made for using numerical simulations to solve QCD, the regnant theory describing the interactions between quarks and gluons. I present an overview of what these calculations involve, why they are hard, and why they are tailor made for parallel computers. Finally, I try to communicate the excitement amongst the practitioners by giving examples of the quantities we will be able to calculate to within a few percent accuracy in the next five years.

Rajan Gupta

1999-05-20

476

New Phenomena in NC Field Theory and Emergent Spacetime Geometry

We give a brief review of two nonperturbative phenomena typical of noncommutative field theory which are known to lead to the perturbative instability known as the UV-IR mixing. The first phenomena concerns the emergence/evaporation of spacetime geometry in matrix models which describe perturbative noncommutative gauge theory on fuzzy backgrounds. In particular we show that the transition from a geometrical background to a matrix phase makes the description of noncommutative gauge theory in terms of fields via the Weyl map only valid below a critical value g*. The second phenomena concerns the appearance of a nonuniform ordered phase in noncommutative scalar {phi}{sup 4} field theory and the spontaneous symmetry breaking of translational/rotational invariance which happens even in two dimensions. We argue that this phenomena also originates in the underlying matrix degrees of freedom of the noncommutative field theory. Furthermore it is conjectured that in addition to the usual WF fixed point at {theta} = 0 there must exist a novel fixed point at {theta} = {infinity} corresponding to the quartic hermitian matrix model.

Ydri, Badis [Institute of Physics BM Annaba University, BP 12-23000-Annaba (Algeria)

2010-10-31

477

Quantum Field Theory in Curved Spacetime

NASA Astrophysics Data System (ADS)

List of contributors; Foreword J. T. Francis Thackeray; 1. African genesis: an evolving paradigm Sally C. Reynolds; 2. Academic genealogy Peter Ungar and Phillip V. Tobias; Part I. In Search of Origins: Evolutionary Theory, New Species, and Paths into the Past: 3. Speciation in hominin evolution Colin Groves; 4. Searching for a new paradigm for hominid origins in Chad (Central Africa) Michel Brunet; 5. From hominoid arboreality to hominid bipedalism Brigitte Senut; 6. Orrorin and the African ape/hominid dichotomy Martin Pickford; 7. A brief history and results of 40 years of Sterkfontein excavations Ronald J. Clarke; Part II. Hominin Morphology Through Time: Brains, Bodies and Teeth: 8. Hominin brain evolution, 1925-2011: an emerging overview Dean Falk; 9. The issue of brain reorganisation in Australopithecus and early hominids: Dart had it right Ralph L. Holloway; 10. The mass of the human brain: is it a spandrel? Paul R. Manger, Jason Hemingway, Muhammad Spocter and Andrew Gallagher; 11. Origin and diversity of early hominin bipedalism Henry M. McHenry; 12. Forelimb adaptations in Australopithecus afarensis Michelle S. M. Drapeau; 13. Hominin proximal femur morphology from the Tugen Hills to Flores Brian G. Richmond and William L. Jungers; 14. Daily rates of dentine formation and root extension rates in Paranthropus boisei, KNM-ER 1817, from Koobi Fora, Kenya M. Christopher Dean; 15. On the evolutionary development of early hominid molar teeth and the Gondolin Paranthropus molar Kevin L. Kuykendall; 16. Digital South African fossils: morphological studies using reference-based reconstruction and electronic preparation Gerhard W. Weber, Philipp Gunz, Simon Neubauer, Philipp Mitteroecker and Fred L. Bookstein; Part III. Modern Human Origins: Patterns, and Processes: 17. Body size in African Middle Pleistocene Homo Steven E. Churchill, Lee R. Berger, Adam Hartstone-Rose and Headman Zondo; 18. The African origin of recent humanity Milford H. Wolpoff and Sang-Hee Lee; 19. Assimilation and modern human origins in the African peripheries Fred H. Smith, Vance T. Hutchinson and Ivor Jankovi?; 20. Patterns of Middle Pleistocene hominin evolution in Africa and the emergence of modern humans Emma Mbua and Günter Bräuer; 21. Integration of the genetic, anatomical, and archaeological data for the African origin of modern humans: problems and prospects Osbjorn M. Pearson; Part IV. In Search of Context: Hominin Environments, Behaviour and Lithic Cultures: 22. Animal palaeocommunity variability and habitat preference of robust australopiths in South Africa Darryl J. de Ruiter, Matt Sponheimer and Julia Lee-Thorp; 23. Impacts of environmental change and community ecology on the composition and diversity of the southern African monkey fauna from the Plio-Pleistocene to the present Sarah Elton; 24. African genesis revisited: reflections on Raymond Dart and the 'Predatory Transition from Ape(-Man) to Man' Travis R. Pickering; 25. Shared intention in early artefacts: an exploration of deep structure and implications for communication and language John A. J. Gowlett; 26. Sibudu Cave: recent archaeological work on the Middle Stone Age Lyn Wadley; 27. The oldest burials and their significance Avraham Ronen; Index.

Reynolds, Sally C.; Gallagher, Andrew

2012-03-01

478

Two-dimensional topological field theories coupled to four-dimensional BF theory

Four dimensional BF theory admits a natural coupling to extended sources supported on two dimensional surfaces or string world-sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two dimensional world-sheet. We show how two dimensional Yang-Mills degrees of freedom can be added on the world-sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world-sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background independent quantum field theory where local degrees of freedom at low energies arise from global topological (world-sheet) degrees of freedom at the fundamental level.

Merced Montesinos; Alejandro Perez

2007-11-19

479

?N?NN weak interaction in effective-field theory

NASA Astrophysics Data System (ADS)

The nonleptonic weak ? ?S ? =1 ?N interaction, responsible for the dominant nonmesonic decay of all but the lightest hypernuclei, is studied in the framework of an effective-field theory. The long-range physics is described through tree-level exchange of the SU(3) Goldstone bosons, while the short-range potential is parametrized in terms of the lowest-order contact terms. We obtain reasonable fits to available weak hypernuclear decay rates and quote the values for the parity-violating asymmetry as predicted by the present effective-field theory.

Parreño, Assumpta; Bennhold, Cornelius; Holstein, Barry R.

2004-11-01

480

Kadyshevsky Field Theory ---Derivative-Interactions and Functional Integral Formalism---

NASA Astrophysics Data System (ADS)

Field theoretical topics are discussed and introduced in the framework of the Quantum Field Theory as developed by Kadyshevsky. In the