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1

Einstein's Theory of Gravitation as a Lagrangian Theory for Tensor Fields

NASA Astrophysics Data System (ADS)

Einstein's theory of gravitation (ETG) is considered as a Lagrangian theory of tensor fields over (pseudo) Riemannian spaces without torsion (Vn spaces, n=4) by means of the method of Lagrangians with covariant derivarives (MLCD). In a trivial manner Euler-Lagrange's equations as Einstein's equations are obtained. The corresponding energy-momentum tensors (EMT's) are found for the standard for the ETG Lagrangian invariant on the basis of the covariant Noether identities. The symmetric energy-momentum tensor of Hilbert appears as an element irrelevant to the whole scheme of the considered Lagrangian thoery of tensor fields over Vn spaces despite of the fact that it has some elements of the structure of the variational EMT of Euler-Lagrange. The notion of the active gravitational rest mast density is related to the variational EMT of Euler-Lagrange and on this basis to a certain extent to the EMT of Hilbert.

Manoff, S.

2

Conditions for the existence of a Lagrangian in field theory

The necessary and sufficient conditions for a given set of n second-order field equations to be derivable from a variational principle of Hamilton's type were derived recently by Santilli. An alternative form is given which makes practical verification less tedious, and permits a direct construction of the Lagrangian.

Farias, J.R.

1982-12-15

3

The Lagrangian-space Effective Field Theory of large scale structures

NASA Astrophysics Data System (ADS)

We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of extended objects in Lagrangian space. In LEFT the resulting finite size effects are described using a multipole expansion parameterized by a set of time dependent coefficients and organized in powers of the ratio of the wavenumber of interest k over the non-linear scale kNL. The multipoles encode the effects of the short distance modes on the long-wavelength universe and absorb UV divergences when present. There are no IR divergences in LEFT. Some of the parameters that control the perturbative approach are not assumed to be small and can be automatically resummed. We present an illustrative one-loop calculation for a power law universe. We describe the dynamics both at the level of the equations of motion and through an action formalism.

Porto, Rafael A.; Senatore, Leonardo; Zaldarriaga, Matias

2014-05-01

4

By using the Girvin-MacDonald effective Lagrangian for the Hall fluid system at filling nu = 1 we are able to evaluate the ground-state energy for a cylinder of infinite length. That is done by using the topological properties of the edge vacuum in the thermodynamic limit, Ne --> ?, nu = 1 fixed, From the vacuum energy we extract the

G. Cristofano; D. Giuliano; G. Maiella

1994-01-01

5

Effective Lagrangians in classical Yang-Mills theories

The formalism of nonlinear electrodynamics is adapted to the Yang-Mills field theory and it is shown that vacuum polarization effects can be described classically through an effective Lagrangian. As an example, an ad hoc Lagrangian is proposed which leads to a simple solution corresponding to a linear plus Coulomb type potential.

Hacyan, S. [Universidad Nacional Autonoma de Mexico (Mexico)

1995-01-01

6

NASA Astrophysics Data System (ADS)

In this Communication, we present a class of Brans-Dicke-like theories with a universal coupling between the scalar field and the matter Lagrangian. We show this class of theories naturally exhibits a decoupling mechanism between the scalar field and matter. As a consequence, this coupling leads to almost the same phenomenology as general relativity in the Solar System: the trajectories of massive bodies and the light propagation differ from general relativity only at the second post-Newtonian order. Deviations from general relativity are beyond present detection capabilities. However, this class of theories predicts a deviation of the gravitational redshift at a level detectable by the future ACES and STE/QUEST missions.

Minazzoli, Olivier; Hees, Aurélien

2013-08-01

7

Lagrangian theory of composite particles

Distinctions between elementary and composite particles within the ; context of the Feynman-Dyson type of S-matrix theory are considered. ; Requirements that the bare coupling constant for the interaction of a composite ; particle and its elementary constituents should vanish and that there should be ; no mass renormalization for a composite particle are exploited. Results ; corroborate Feynman's principle

A. Salam

1962-01-01

8

NASA Astrophysics Data System (ADS)

Preface; Introduction; 1. Classical fields, symmetries and their breaking; 2. Path integral formulation of quantum field theory; 3. Feynman rules for Yang-Mills theories; 4. Introduction to the theory of renormalization; 5. Quantum electrodynamics; 6. Renormalization group; 7. Scale invariance and operator product expansion; 8. Quantum chromodynamics; 9. Chiral symmetry, spontaneous symmetry breaking; 10. Spontaneous and explicit global symmetry breaking; 11. Higgs mechanisms in gauge theories; 12. Standard electroweak theory; 13. Chiral anomalies; 14. Effective lagrangians; 15. Introduction to supersymmetry; Appendices.

Pokorski, Stefan

2000-03-01

9

Using Lagrangian Perturbation Theory for Precision Cosmology

NASA Astrophysics Data System (ADS)

We explore the Lagrangian perturbation theory (LPT) at one-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum LPT. Our approximate solution has good convergence in the series expansion and enables us to compute the power spectrum in LPT accurately and quickly. Non-linear corrections in this theory naturally satisfy the law of conservation of mass because the relation between matter density and the displacement vector of dark matter corresponds to the conservation of mass. By matching the one-loop solution in LPT to the two-loop solution in standard perturbation theory, we present an approximate solution of the power spectrum which has higher order corrections than the two-loop order in standard perturbation theory with the conservation of mass satisfied. With this approximation, we can use LPT to compute a non-linear power spectrum without any free parameters, and this solution agrees with numerical simulations at k = 0.2 h Mpc–1 and z = 0.35 to better than 2%.

Sugiyama, Naonori S.

2014-06-01

10

Perturbative Coherence in Field Theory.

National Technical Information Service (NTIS)

A general condition for coherent quantization by perturbative methods is given, because the basic field equations of a fild theory are not always derivable from a Lagrangian. It's seen that non-lagrangian models way have well defined vertices, provided th...

R. Aldrovandi R. A. Kraenkel

1987-01-01

11

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

12

Introduction to Symplectic Field Theory

We sketch in this article a new theory, which we call Symplectic Field Theory or SFT, which provides an approach to Gromov-Witten invariants of symplectic manifolds and their Lagrangian submanifolds in the spirit of topological field theory, and at the same time serves as a rich source of new invariants of contact manifolds and their Legendrian submanifolds. Moreover, we hope

Yakov Eliashberg; Alexander Givental; Helmut Hofer

2000-01-01

13

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

14

The paper develops a thermodynamic and thermostatic theory for thermoelastic electromagnetic solids along the lines of the theory of Liu and Mueller (1972) for fluids in electromagnetic fields. The Maxwell equations are derived in material (or Lagrangian) form with attention given to transformation properties under Euclidean transformations of the spatial frames. A material description of the balance laws of mechanics

Kolumban Hutter

1975-01-01

15

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

16

An exact Lagrangian integral for the Newtonian gravitational field strength

NASA Astrophysics Data System (ADS)

An exact expression for the gravitational field strength in a self-gravitating dust continuum is derived within the Lagrangian picture of continuum mechanics. From the Euler Newton system a transport equation for the gravitational field strength is formulated and then integrated along trajectories of continuum elements. The resulting integral solves one of the Lagrangian equations of the corresponding Lagrange Newton system in general. Relations to known exact solutions without symmetry in Newtonian gravity are discussed. The presented integral may be employed to access the nonperturbative regime of structure formation in Newtonian cosmology, and to apply iterative Lagrangian schemes to solve the Lagrange Newton system.

Buchert, Thomas

2006-05-01

17

Renormalisation of gauge theories using effective Lagrangians, II

NASA Astrophysics Data System (ADS)

The method of effective Lagrangian flow provides the most physically illuminating discussion of renormalisation theory. The extra complication of the unitarity question in gauge theories was solved in the first paper (for the non-chiral case) and in this paper we extend the results to chiral gauge theories and rigid N = 1 super Yang-Mills. We prove that one-loop anomaly cancellation is a sufficient condition for unitarity, and we also prove the Adler-Bardeen theorem for the divergence of a non-gauged axial current. Finally, we show that the gravitational anomalies of a gauged current are removed completely when canceled at the one-loop level.

Warr, Brian J.

1988-04-01

18

a Note on the - Invariant Lagrangian Densities for the Free Abelian 2-FORM Gauge Theory

NASA Astrophysics Data System (ADS)

We show that the previously known off-shell nilpotent (s(a)b2 = 0) and absolutely anticommuting (sb sab + sab sb = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci-Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler-Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.

Gupta, Saurabh; Malik, R. P.

19

NASA Astrophysics Data System (ADS)

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.

Costa-Quintana, J.; López-Aguilar, F.

2012-08-01

20

Bilocal field theory in four dimensions

A bilocal field theory having Moebius gauge invariance is proposed. In four dimensions there exists a zero momentum state of the first-quantized model which belongs to a nontrivial BRS cohomology class. A field theory Lagrangian having gauge invariance only in four dimensions is constructed.

Hori, T. (Institute of Physics, Teikyo University, Otsuka 359, Hachioji-shi, Tokyo 192-03 (Japan))

1993-07-15

21

Friedmann Models and Cosmological Solutions in the Bimetric Theory with a Quadratic Lagrangian

Cosmological models are investigated within the framework of the bimetric theory of gravitation with a Lagrangian that is quadratic with respect to “intensities” gik|l. It is shown that the theory predicts not only singular but also nonsingular solutions.

A. H. Yeranyan

2001-01-01

22

Propagating modes in gauge field theories of gravity

The particle content of the most general quadratic field Lagrangian for Poincaré gauge field theories is examined and restrictions on the coupling constants for absence of ghosts and tachyons are derived. Our final field Lagrangian contains three coupling constants, the usual gravitational constant in front of an Einsteinian part and two other constants governing pure torsion terms.

R. Kuhfuss; J. Nitsch

1986-01-01

23

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

24

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

25

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

26

Modelling non-linear evolution using Lagrangian perturbation theory re-expansions

NASA Astrophysics Data System (ADS)

We present a new method to calculate formation of cosmological structure in the Newtonian limit. The method is based on Lagrangian perturbation theory (LPT) plus two key theoretical extensions. One advance involves identifying and fixing a previously ignored gauge-like degree of freedom relating quantities calculated in LPT to those measured by a preferred Friedmann-Robertson-Walker observer. Handling this connection between calculational and observer frames is physically essential and ensures a momentum conserving description. The second extension is to systematically re-expand the equations of motion to increase LPT's radius of convergence to the maximum future time prior to orbit crossing. The paper implements a complete algorithm and performs extensive `proof of principle' tests of the new method, including direct comparison to known solutions, evaluation of conserved quantities and formal convergence studies. All are satisfactory. We show that convergence is exponential in grid size and Lagrangian order and polynomial in step size. There are three powerful advantages afforded by the new technique: (1) it employs a smooth representation of all fields, and the results are not limited by particle induced shot-noise errors, (2) it permits the numerical error to be controlled by changing Lagrangian order and/or number of steps allowing, in principle, arbitrarily small errors to be achieved prior to orbit crossing and (3) it handles generic cold initial data (any periodic density and velocity fields, including those with initial rotational components). Together, these properties make the new technique well suited to handle quasi-linear scales where analytic methods and/or numerical simulations fail to provide suitably accurate answers.

Nadkarni-Ghosh, Sharvari; Chernoff, David F.

2013-05-01

27

Friedmann Models and Cosmological Solutions in the Bimetric Theory with a Quadratic Lagrangian

Cosmological models are investigated within the framework of the bimetric theory of gravitation with a Lagrangian that is quadratic with respect to intensities g ik|l . It is shown that the theory predicts not only singular but also nonsingular solutions.

A. H. Yeranyan

2001-01-01

28

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

29

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

30

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

NASA Technical Reports Server (NTRS)

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Buchert, T.; Melott, A. L.; Weiss, A. G.

1993-01-01

31

An augmented Lagrangian method for a class of LMI-constrained problems in robust control theory

This paper present a new approach to solve a class of nonconvex LMI-constrained problem in robust control theory. The problems we consider may be recast as the minimization of a linear objective subject to linear matrix inequality (LMI) constraints in tandem with nonconvex constraints related to rank conditions. We solve these problems using an extension of the augmented Lagrangian technique.

B. Fares; P. Apkariant; D. Nolfl

2000-01-01

32

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

33

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

34

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

35

NASA Astrophysics Data System (ADS)

We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the BRST-BFV approach suggested for bosonic fields in our first article [I.L. Buchbinder, A. Reshetnyak, Nucl. Phys. B 862 (2012) 270, arXiv:1110.5044 [hep-th

Reshetnyak, A.

2013-04-01

36

Generalized Lee-Wick formulation from higher derivative field theories

We study a higher derivative (HD) field theory with an arbitrary order of derivative for a real scalar field. The degree of freedom for the HD field can be converted to multiple fields with canonical kinetic terms up to the overall sign. The Lagrangian describing the dynamics of the multiple fields is known as the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to the original HD Lagrangian up to the quantum level. Until now, the AF Lagrangian has been studied only for N=2 and 3 cases, where N is the number of poles of the two-point function of the HD scalar field. We construct the AF Lagrangian for arbitrary N. By the linear combinations of AF fields, we also obtain the corresponding LW form. We find the explicit mapping matrices among the HD fields, the AF fields, and the LW fields. As an exercise of our construction, we calculate the relations among parameters and mapping matrices for N=2, 3, and 4 cases.

Cho, Inyong; Kwon, O-Kab [School of Liberal Arts, Seoul National University of Technology, Seoul 139-743 (Korea, Republic of); Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of)

2010-07-15

37

Lagrangian neoclassical transport theory applied to the region near the magnetic axis

NASA Astrophysics Data System (ADS)

Neoclassical transport theory around the magnetic axis of a tokamak is studied, in which relatively wide ``potato'' orbits play an important role in transport. Lagrangian formulation of transport theory, which has been investigated to reflect finiteness of guiding-center orbit widths to transport equations, is developed in order to analyze neoclassical transport near the axis for a low-collisionality plasma. The treatment of self-collision term in Lagrangian formulation is revised to retain momentum conservation property of it. By directly reflecting the orbital properties of all the types of orbits in calculation, the ion thermal conductivity around the axis is found to decrease from that predicted by conventional neoclassical theory. This result supports recent numerical simulations which show the reduction of thermal conductivity near the magnetic axis.

Satake, Shinsuke; Okamoto, Masao; Sugama, Hideo

2002-09-01

38

Strings on pp-waves and massive two dimensional field theories

We find a general class of pp-wave solutions of type IIB string theory such that the light cone gauge worldsheet lagrangian is that of an interacting massive field theory. When the light cone Lagrangian has (2,2) supersymmetry we can find backgrounds that lead to arbitrary superpotentials on the worldsheet. We consider situations with both flat and curved transverse spaces. We

Juan Maldacena; Liat Maoz

2002-01-01

39

NASA Astrophysics Data System (ADS)

Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms even for nonlinear and non-Gaussian signal inference problems. IFT algorithms exploit spatial correlations of the signal fields and benefit from techniques developed to investigate quantum and statistical field theories, such as Feynman diagrams, re-normalisation calculations, and thermodynamic potentials. The theory can be used in many areas, and applications in cosmology and numerics are presented.

Enßlin, Torsten

2013-08-01

40

Dual field theory of strong interactions

A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac charge g = (137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector boson W/sup +/-/. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant ..cap alpha.. = 1/137.

Akers, D.

1987-07-01

41

Augmented Lagrangian method for constrained nuclear density functional theory

NASA Astrophysics Data System (ADS)

The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of multi-dimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves the accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia; and is well adapted to supercomputer applications.

Staszczak, A.; Stoitsov, M.; Baran, A.; Nazarewicz, W.

2010-10-01

42

We argue that Feynman's Integral imposes the condition of being mutually unbiased on pairs of bases that are causally proximal. This sheds light on the nature of Lagrangian theories from the emergent space-time perspective.

Svetlichny, George [Departamento de Matematica, Pontificia Universidade Catolica, Rio de Janeiro (Brazil)

2007-11-14

43

Special symmetries for the Utiyama Lagrangian with external Yang-Mills fields

NASA Astrophysics Data System (ADS)

This paper demonstrates how conditions for the existence of symmetries for particles interacting with external background gauge fields arise easily from the standard symmetry equations. The general phenomenon is described by the Lagrangian LUA obtained from Utiyama's original Lagrangian LU by regarding the gauge fields A as a given set of fields. An infinitesimal transformation X+Y, consisting of certain combined infinitesimal coordinate and local gauge transformations, will be an infinitesimal symmetry of LUA precisely when the Lie derivative &(LUA) yields a Lagrangian with identically vanishing Euler-Lagrange equations. This Lie derivative is explicitly computed and is shown to contain the expressions derived recently by several papers in the literature, as well as a new expression with possible physical importance.

Betounes, David E.

1985-05-01

44

Attractive Lagrangians for noncanonical inflation

Treating inflation as an effective theory, we expect the effective Lagrangian to contain higher-dimensional kinetic operators suppressed by the scale of UV physics. When these operators are powers of the inflaton kinetic energy, the scalar field can support a period of noncanonical inflation which is smoothly connected to the usual slow-roll inflation. We show how to construct noncanonical inflationary solutions to the equations of motion for the first time, and demonstrate that noncanonical inflation is an attractor in phase space for all small- and large-field models. We identify some sufficient conditions on the functional form of the Lagrangian that lead to successful noncanonical inflation since not every Lagrangian with higher-dimensional kinetic operators can support noncanonical inflation. This extends the class of known viable Lagrangians and excludes many Lagrangians which do not work.

Franche, Paul; Underwood, Bret; Wissanji, Alisha [Department of Physics, McGill University, 3600 University Street, Montreal, Quebec, H3A 2T8 (Canada); Gwyn, Rhiannon [Department of Physics, King's College London, Strand, London WC2R 2LS (United Kingdom)

2010-06-15

45

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

46

(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

47

We review the generalization of field theory to space-time with noncommuting\\u000acoordinates, starting with the basics and covering most of the active\\u000adirections of research. Such theories are now known to emerge from limits of M\\u000atheory and string theory, and to describe quantum Hall states. In the last few\\u000ayears they have been studied intensively, and many qualitatively new

Michael R. Douglas; Nikita A. Nekrasov

2001-01-01

48

Lagrangian perturbation theory for cosmological fluid describes structure formation in the quasinonlinear stage well. In a previous paper, we presented a third-order perturbative equation for Lagrangian perturbation with pressure. There we considered only the longitudinal modes for the first-order perturbation. In this paper, we generalize the perturbation, i.e., we consider both the longitudinal and the transverse modes for the first-order perturbation. Then we derive third-order perturbative equations and solutions.

Tatekawa, Takayuki [Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555 (Japan); Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555 (Japan); Department of Physics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo, Tokyo 112-8610 (Japan)

2005-07-15

49

NASA Technical Reports Server (NTRS)

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

Melott, A. L.; Buchert, T.; Weib, A. G.

1995-01-01

50

Geometrical thermodynamic field theory

NASA Astrophysics Data System (ADS)

A manifestly covariant, coordinate independent reformulation of the thermodynamic field theory (TFT) is presented. The TFT is a covariant field theory that describes the evolution of a thermodynamic system, extending the near-equilibrium theory established by Prigogine in 1954. We introduce the minimum rate of dissipation principle, which applies to any system relaxing toward a steady state. We also derive the thermodynamic field equations, which in the case of ?-? and ?-? processes have already appeared in the literature. In more general cases, the equations are notably simpler than those previously encountered, and they extend beyond the weak-field regime. Finally, we derive the equations that determine the steady states as well as the critical values of the control parameters beyond which a steady state becomes unstable.

Sonnino, Giorgio; Evslin, Jarah

51

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

52

Electroweak chiral Lagrangian and [ital CP]-violating effects in technicolor theories

We estimate the [ital CP]-violating [ital WW][gamma] and [ital WWZ] anomalous form factors, arising from [ital CP]-violating interactions in extended technicolor theories, and discuss their future experimental detectability. The electric dipole moment of the [ital W] boson is found to be as large as [similar to]10[sup [minus]21] [ital e] cm. We connect the [ital CP]-odd [ital WW][gamma] and [ital WWZ] couplings to the corresponding [ital CP]-violating electroweak chiral Lagrangian operators. The electric dipole moments of the neutron and the electron in technicolor theories are estimated to be as large as [similar to]10[sup [minus]26] and [similar to]10[sup [minus]29] cm, respectively. We also suggest the potential to observe large [ital CP]-violating technicolor effects in the decay [ital t][r arrow][ital b]+[ital W][sup +].

Appelquist, T.; Wu, G. (Department of Physics, Yale University, New Haven, Connecticut 06520 (United States))

1995-01-01

53

BRST-invariant Lagrangian of spontaneously broken gauge theories in a noncommutative geometry

The quantization of spontaneously broken gauge theories in a noncommutative geometry (NCG) has been sought for some time, because quantization is crucial for making the NCG approach a reliable and physically acceptable theory. Lee, Hwang, and Ne{close_quote}eman recently succeeded in realizing the BRST quantization of gauge theories in a NCG in the matrix derivative approach proposed by Coquereaux and co-workers. The present author has proposed a characteristic formulation to reconstruct a gauge theory in a NCG on the discrete space {ital M}{sub 4}{times}{ital Z}{sub {sub {ital N}}}. Since this formulation is a generalization of the differential geometry on the ordinary manifold to that on the discrete manifold, it is more familiar than other approaches. In this paper, we show that within our formulation we can obtain the BRST-invariant Lagrangian in the same way as Lee, Hwang, and Ne{close_quote}eman and apply it to the SU(2){times}U(1) gauge theory. {copyright} {ital 1996 The American Physical Society.}

Okumura, Y. [Department of Natural Science, Chubu University, Kasugai, 487 (Japan)] [Department of Natural Science, Chubu University, Kasugai, 487 (Japan)

1996-09-01

54

Computational quantum field theory

NASA Astrophysics Data System (ADS)

The computational quantum field theory (CQFT) is considered as part of computational physics. The main mathematical structures of the CQFT are described in the case of quantum chromodynamics. As examples of the application of the CQFT methods, the calculation of the topological susceptibility and the gluon condensates are considered.

Makhaldiani, N. V.

55

Computational Quantum Field Theory.

National Technical Information Service (NTIS)

The computational quantum field theory (CQFT) is considered as a part of the computational physics. The main mathematical structures of the CQFT are described in the case of quantum chromodynamics. As examples of the application of the CQFT methods the ca...

N. V. Makhaldiani

1986-01-01

56

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

57

The author constructs a non-Abelian field theory by gauging a Kac-Moody algebra, obtaining an infinite tower of interacting vector fields and associated ghosts, that obey slightly modified Feynman rules. She discusses the spontaneous symmetry breaking of such theory via the Higgs mechanism. If the Higgs particle lies in the Cartan subalgebra of the Kac-Moody algebra, the previously massless vectors acquire a mass spectrum that is linear in the Kac-Moody index and has additional fine structure depending on the associated Lie algebra. She proceeds to show that there is no obstacle in implementing the affine extension of supersymmetric Yang-Mills theories. The result is valid in four, six and ten space-time dimensions. Then the affine extension of supergravity is investigated. She discusses only the loop algebra since the affine extension of the super-Poincare algebra appears inconsistent. The construction of the affine supergravity theory is carried out by the group manifold method and leads to an action describing infinite towers of spin 2 and spin 3/2 fields that interact subject to the symmetries of the loop algebra. The equations of motion satisfy the usual consistency check. Finally, she postulates a theory in which both the vector and scalar fields lie in the loop algebra of SO(3). This theory has an expanded soliton sector, and corresponding to the original 't Hooft-Polyakov solitonic solutions she now finds an infinite family of exact, special solutions of the new equations. She also proposes a perturbation method for obtaining an arbitrary solution of those equations for each level of the affine index.

Cadavid, A.C.

1989-01-01

58

NASA Astrophysics Data System (ADS)

We present a tool for daily validation of modeled or satellite derived velocity fields in the southeastern region of the Mediterranean. Within this tool, spatial patterns of Lagrangian Coherent Structures (LCS) derived from the velocity field are compared to distribution patterns of satellite derived surface chlorophyll. This comparison is advantageous to pollution spread predictions since it compares the location of fronts in passive tracer spread. The suggested methodology is based on Lagrangian tools that were shown to be very effective in reconstructing the specific effect of horizontal stirring on individual oceanic patterns. Lagrangian techniques are based, in general, on the identification of the velocity field characteristics along particle trajectories. They are well suited for diagnosing properties of tracers like chlorophyll, since they allow to quantify the dynamical properties experienced by a parcel of water during its motion. The Lagrangian diagnostics performed in this tool are based on analyzing the spatial structure of LCS from calculation of finite size Lyapunov exponents (FSLE). These LCS induce in advected tracer fields filament patterns with typical length in the range of 10 - 100 km and lifetime in the range of days/weeks (though it can be much longer if the patterns are associated to long-lived and energetic mesoscale features with low temporal variability). Since LCS represent transport barriers and tracer boundaries, they separate between water bodies with possibly different physical - biogeochemical properties. Daily analyses ( available online at http://isramar.ocean.org.il/isramar2009/cosem/fsle.aspx ) of LCS is performed on AVISO altimetry derived velocity fields and on operational numerical circulation forecasts, which are produced as part of the South Eastern Levantine Israeli Prediction System (SELIPS). The LCS analyses are then placed atop maps of surface Chlorophyll concentrations, which is provided within the MyOcean project. A subjective scoring criteria for the fit quality is formulated and implemented for a year of validating circulation estimates in the southeastern Levantine.

Goldman, Ron; Efrati, Shai; Lehahn, Yoav; Gertman, Isaac; Heifetz, Eyal

2014-05-01

59

Inductive approach towards a phenomenologically more satisfactory unififed field theory

A unified field theory constituting a fusion of the ideas of supersymmetries with general relativity and gauge theory is investigated. A Lagrangian formalism is constructed step by step; the last step consists in a marriage with Kaluza's idea of a multidimensional space-time. Our aim is not to achieve a full local supersymmetry in eleven dimensions, but rather to attain a compromise with the symmetries of the fundamental interactions either known phenomenologically, or only suspected to exist in nature.

Rayski, J.; Rayski J.M. Jnr.

1985-11-01

60

Hybrid conformal field theories

NASA Astrophysics Data System (ADS)

We describe a class of (2,2) superconformal field theories obtained by fibering a Landau-Ginzburg orbifold CFT over a compact Kähler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model, our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of linear models and comparing spectra among the phases.

Bertolini, Marco; Melnikov, Ilarion V.; Plesser, M. Ronen

2014-05-01

61

During the month of August 1978, two Lagrangian measurement platform (LAMP) experiments were conducted in conjunction with the Environmental Protection Agency's Tennessee Plume Study. In both experiments, the LAMP was launched into the Cumberland Power Plant plume. The instrumented balloon system provided data on the chemical and physical behavior of the pollutants downwind from the plant over the duration of the flights. A description of the field effort, the data acquired, and some preliminary results are presented here.

Gay, G.T.; Zak, B.D.; Barker, B.; Holland, R.M. Jr.; Homann, P.S.

1981-03-01

62

Linear Stability of Elliptic Lagrangian Solutions of the Planar Three-Body Problem via Index Theory

NASA Astrophysics Data System (ADS)

It is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass parameter {?=27(m_1m_2+m_2m_3+m_3m_1)/(m_1+m_2+m_3)^2 in [0, 9]} and the eccentricity {e in [0, 1)} . We are not aware of any existing analytical method which relates the linear stability of these solutions to the two parameters directly in the full rectangle [0, 9] × [0, 1), aside from perturbation methods for e > 0 small enough, blow-up techniques for e sufficiently close to 1, and numerical studies. In this paper, we introduce a new rigorous analytical method to study the linear stability of these solutions in terms of the two parameters in the full (?, e) range [0, 9] × [0, 1) via the ?-index theory of symplectic paths for ? belonging to the unit circle of the complex plane, and the theory of linear operators. After establishing the ?-index decreasing property of the solutions in ? for fixed {ein [0, 1)} , we prove the existence of three curves located from left to right in the rectangle [0, 9] × [0, 1), among which two are -1 degeneracy curves and the third one is the right envelope curve of the ?-degeneracy curves, and show that the linear stability pattern of such elliptic Lagrangian solutions changes if and only if the parameter (?, e) passes through each of these three curves. Interesting symmetries of these curves are also observed. The linear stability of the singular case when the eccentricity e approaches 1 is also analyzed in detail.

Hu, Xijun; Long, Yiming; Sun, Shanzhong

2014-05-01

63

Algebraic orbifold conformal field theories

The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank

Feng Xu

2000-01-01

64

NASA Astrophysics Data System (ADS)

The paper presents rate constitutive theories for finite deformation of homogeneous, isotropic, compressible, and incompressible thermoviscoelastic solids without memory in Lagrangian description derived using the second law of thermodynamics expressed in terms of Gibbs potential ?. To ensure thermodynamic equilibrium during evolution, the rate constitutive theories must be derived using entropy inequality [as other three conservation and balance laws are do not provide a mechanism for deriving constitutive theories for the deforming matter (Surana in Advanced mechanics of continuua. in preparation, 2014)]. The two forms of the entropy inequality in ? derived using conjugate pairs {mathbf{?}^*} , {[dot{J}]} : first Piola-Kirchhoff stress tensor and material derivative of the Jacobian of deformation and {mathbf{?}^{[0]}} , {dot{mathbf{\\varepsilon}}_{[0]}} ; second Piola-Kirchhoff stress tensor and material derivative of Green's strain tensor are precisely equivalent as the conjugate pairs {mathbf{?}^*} , {[dot{J}]} and {mathbf{?}^{[0]}} , {dot{mathbf{\\varepsilon}}_{[0]}} are transformable from each other. In the present work, we use {mathbf{?}^{[0]}} , {dot{mathbf{\\varepsilon}}_{[0]}} as conjugate pair. Two possible choices of dependent variables in the constitutive theories: ?, ?, {mathbf{?}^{[0]}} , {mathbf{q}} and ?, ?, {mathbf{\\varepsilon}_{[0]}} , {mathbf{q}} (in which ? is entropy density and {mathbf{q}} is heat vector) are explored based on conservation and balance laws. It is shown that the choice of ?, ?, {mathbf{\\varepsilon}_{[0]}} , {mathbf{q}} is essential when the entropy inequality is expressed in terms of ?. The arguments of these dependent variables are decided based on desired physics. Viscoelastic behavior requires considerations of at least {mathbf{\\varepsilon}_{[0]}} and {dot{mathbf{\\varepsilon}}_{[0]}} (or {mathbf{\\varepsilon}_{[1]}} ) in the constitutive theories. We generalize and consider strain rates {mathbf{\\varepsilon}_{[i]}} ; i = 0, 1, …, n-1 as arguments of the dependent variables in the derivations of the ordered rate theories of up to orders n. At the onset, {mathbf{?}^{[0]}} , {mathbf{\\varepsilon}_{[i]}} ; i = 0, 1, …, n-1, ? and {mathbf{g}} are considered as arguments of ?, ?, {mathbf{\\varepsilon}_{[n]}} and {mathbf{q}} . When {dot{?}} is substituted in the entropy inequality, the resulting conditions eliminate ? as a dependent variable, reduce arguments of some of the dependent variables in the constitutive theory etc. but do not provide a mechanism to derive constitutive theories for {mathbf{\\varepsilon}_{[i]}} and {mathbf{q}} . The stress tensor {mathbf{?}^{[0]}} is decomposed into equilibrium stress {{}_e mathbf{?}^{[0]}} and deviatoric stress {{}_d mathbf{?}^{[0]}} . Upon substituting this in the entropy inequality, we finally arrive at the inequality that must be satisfied by {{}_e mathbf{?}^{[0]}} , {{}_d mathbf{?}^{[0]}} and {mathbf{q}} . Derivations of the constitutive theory for {{}_e mathbf{?}^{[0]}} follow directly from {{}_e mathbf{?}^{(0)}} , equilibrium Cauchy stress tensor, and the constitutive theory for {mathbf{\\varepsilon}_{[n]}} is derived using the theory of generators and invariants. Constitutive theories for the heat vector {mathbf{q}} of up to orders n that are consistent (in terms of the argument tensors) with the constitutive theories for {mathbf{\\varepsilon}_{[n]}} are also derived. Many simplified forms of the rate theories of orders n are presented. Material coefficients are derived by considering Taylor series expansions of the coefficients in the linear combinations representing {mathbf{\\varepsilon}_{[n]}} and {mathbf{q}} using the combined generators of the argument tensors about a known configuration {\\underline{?}} in the combined invariants of the argument tensors and temperature. It is shown that the rate constitutive theories of order one (n = 1) when further simplified results in constitutive theories that resemble currently used theories but are in fact different. The solid materials characterized by these theories h

Surana, K. S.; Reddy, J. N.; Nunez, D.

2014-06-01

65

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

66

Noncommutative Field Theories and (Super)String Field Theories

In this lecture notes we explain and discuss some ideas concerning noncommutative ge- ometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormaliz- ability and the UV\\/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to

A. A. Giryavets; A. S. Kosheleva; P. B. Medvedeve

67

Noncommutative Field Theories and (super)string Field Theories

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV\\/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations

I. Ya. Aref'eva; D. M. Belov; A. A. Giryavets; A. S. Koshelev; P. B. Medvedev

2002-01-01

68

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

69

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

70

Logarithmic conformal field theory

NASA Astrophysics Data System (ADS)

Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more complicated non-rational theories. Examples include critical percolation, supersymmetric string backgrounds, disordered electronic systems, sandpile models describing avalanche processes, and so on. In each case, the non-rationality and non-unitarity of the CFT suggested that a more general theoretical framework was needed. Driven by the desire to better understand these applications, the mid-1990s saw significant theoretical advances aiming to generalise the constructs of rational CFT to a more general class. In 1994, Nahm introduced an algorithm for computing the fusion product of representations which was significantly generalised two years later by Gaberdiel and Kausch who applied it to explicitly construct (chiral) representations upon which the energy operator acts non-diagonalisably. Their work made it clear that underlying the physically relevant correlation functions are classes of reducible but indecomposable representations that can be investigated mathematically to the benefit of applications. In another direction, Flohr had meanwhile initiated the study of modular properties of the characters of logarithmic CFTs, a topic which had already evoked much mathematical interest in the rational case. Since these seminal theoretical papers appeared, the field has undergone rapid development, both theoretically and with regard to applications. Logarithmic CFTs are now known to describe non-local observables in the scaling limit of critical lattice models, for example percolation and polymers, and are an integral part of our understanding of quantum strings propagating on supermanifolds. They are also believed to arise as duals of three-dimensional chiral gravity models, fill out hidden sectors in non-rational theories with non-compact target spaces, and describe certain transitions in various incarnations of the quantum Hall effect. Other physical applications range from two-dimensional turbulence and non-equilibrium systems to aspects of the AdS/CFT correspondence and describing supersymmetric sigma models beyond the topological sector. We refer the reader to the

Gainutdinov, Azat; Ridout, David; Runkel, Ingo

2013-12-01

71

Computational quantum field theory

NASA Astrophysics Data System (ADS)

I will give an overview on recent attempts to solve the time-dependent Dirac equation for the electron-positron field operator. These numerical solutions permit a first temporally and spatially resolved insight into the mechanisms of how an electron-positron pair can be created from vacuum in a very strong force field. This approach has helped to illuminate a wide range of controversial questions. Some of these questions arise for complicated physical situations such as how an electron scatters off a supercritical potential barrier (Klein paradox). This requires the application of quantum field theory to study the combined effect of the pair-production due to the supercriticality of the potential together with the scattering at the barrier involving the Pauli-principle. Other phenomena include Schr"odinger's Zitterbewegung and the localization problem for a relativistic particle. This work has been supported by the NSF and Research Corporation. P. Krekora, K. Cooley, Q. Su and R. Grobe, Phys. Rev. Lett. 95, 070403 (2005). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 93, 043004 (2004). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 92, 040406 (2004).

Grobe, Rainer

2006-05-01

72

Topics in field theory and string theory.

National Technical Information Service (NTIS)

In the past year, I have continued to investigate the relations between conformal field theories and lattice statistical mechanical models, and in particular have been studying two dimensional models coupled to quantum gravity. I have continued as well to...

1990-01-01

73

Mixing angles of quarks and leptons in quantum field theory

Arguments coming from Quantum Field Theory are supplemented with a 1-loop perturbative calculation to settle the non-unitarity\\u000a of mixing matrices linking renormalized mass eigenstates to bare flavor states for non-degenerate coupled fermions. We simultaneously\\u000a diagonalize the kinetic and mass terms and counterterms in the renormalized Lagrangian. SU(2)\\u000a L\\u000a gauge invariance constrains the mixing matrix in charged currents of renormalized mass

Quentin Duret; Bruno Machet; M. I. Vysotsky

2009-01-01

74

Variational formulation of quantum field theory - I 011

Summary In this paper we present a variational approach to quantum field theory which parallels some recent formulations of statistical\\u000a mechanics. The main interest of this method lies in the fact that the dynamical problem separates naturally into two distinct\\u000a mathematical problems:A) One first determines the structure of the skeleton diagrams generated by a given interaction Lagrangian, using certain functional\\u000a differential

H. D. Dahmen; G. Jona-Lasinio

1967-01-01

75

NASA Astrophysics Data System (ADS)

Chameleons are light scalar fields with remarkable properties. Through the interplay of self-interactions and coupling to matter, chameleon particles have a mass that depends on the ambient matter density. The manifestation of the fifth force mediated by chameleons therefore depends sensitively on their environment, which makes for a rich phenomenology. In this paper, we review two recent results on chameleon phenomenology. The first result a pair of no-go theorems limiting the cosmological impact of chameleons and their generalizations: (i) the range of the chameleon force at cosmological density today can be at most ˜Mpc (ii) the conformal factor relating Einstein- and Jordan-frame scale factors is essentially constant over the last Hubble time. These theorems imply that chameleons have negligible effect on the linear growth of structure, and cannot account for the observed cosmic acceleration except as some form of dark energy. The second result pertains to the quantum stability of chameleon theories. We show how requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound of 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 2 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.

Khoury, Justin

2013-11-01

76

Noncommutative Field Theories and (Super)String Field Theories

In this lecture notes we explain and discuss some ideas concerning\\u000anoncommutative geometry in general, as well as noncommutative field theories\\u000aand string field theories. We consider noncommutative quantum field theories\\u000aemphasizing an issue of their renormalizability and the UV\\/IR mixing. Sen's\\u000aconjectures on open string tachyon condensation and their application to the\\u000aD-brane physics have led to wide investigations

I. Ya. Aref'eva; D. M. Belov; A. A. Giryavets; A. S. Koshelev; P. B. Medvedev

2001-01-01

77

A spherically symmetric electro-vacuum solution of the Poincaré gauge field theory of gravitation

We consider the Poincaré gauge field theory of gravitation with a purely quadratic lagrangian in the case coupled with the electromagnetic field. We solve the field equations to obtain a static spherically symmetric electro-vacuum solution. This solution reduces to Baekler's vacuum solution in the limit beta --> 0, and the metric in this solution reduces to the Reissner-Nordström metric in

Chul H. Lee

1983-01-01

78

Field Theory of Tachyon Matter

We propose a field theory for describing the tachyon on a brane-antibrane system near the minimum of the potential. This field theory realizes two known properties of the tachyon effective action: (a) absence of plane-wave solutions around the minimum, and (b) exponential fall off of the pressure at late time as the tachyon field evolves from any spatially homogeneous initial

Ashoke Sen

2002-01-01

79

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

80

Scalar field theory on noncommutative Snyder spacetime

We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.

Battisti, Marco Valerio [Centre de Physique Theorique, Case 907 Luminy, 13288 Marseille (France); Meljanac, Stjepan [Rudjer Boskovic Institute, Bijenicka c.54, HR-10002 Zagreb (Croatia)

2010-07-15

81

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

82

Dimensional Continuation in Field Theory

The continuation of space-time dimension to an arbitrary complex number is discussed. The ultra-violet and infra-red divergences are simply regularized by analytically continuing to some proper dimension n. Combined with functional integral quantization, it provides a simple and elegant description of quantum field theory. Two well known field theories are discussed. Scalar field theory and quantum electrodynamics. In the scalar

Taeyeon Lee

1988-01-01

83

New Terms for Compact Form of Electroweak Chiral Lagrangian

The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add

Zhang Hong-Hao; Yan Wen-Bin; J. K. Parry; Li Xue-Song

2008-01-01

84

New Terms for the Compact Form of Electroweak Chiral Lagrangian

The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add

Hong-Hao Zhang; Wen-Bin Yan; J. K. Parry; Xue-Song Li

2007-01-01

85

Vector field theories in cosmology

Recently proposed theories based on the cosmic presence of a vectorial field are compared and contrasted. In particular the so-called Einstein aether theory is discussed in parallel with a recent proposal of a strained space-time theory (cosmic defect theory). We show that the latter fits reasonably well the cosmic observed data with only one, or at most two, adjustable parameters, while other vector theories use much more. The Newtonian limits are also compared. Finally we show that the cosmic defect theory may be considered as a special case of the aether theories, corresponding to a more compact and consistent paradigm.

Tartaglia, A.; Radicella, N. [Dipartimento di Fisica del Politecnico and INFN section of Turin Corso Duca degli Abruzzi 24, I-10129 Turin (Italy)

2007-10-15

86

NASA Astrophysics Data System (ADS)

Linear response calculations based on density matrix perturbation theory [A. M. N. Niklasson and M. Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] have been developed within a self-consistent tight-binding method for extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett., 100, 123004 (2008)]. Besides the nuclear coordinates, extended auxiliary electronic degrees of freedom are added to the regular Born-Oppenheimer Lagrangian, both for the electronic ground state and response densities. This formalism enables highly efficient, on-the-fly, analytic computations of the polarizability autocorrelation functions and the Raman spectra during energy conserving Born-Oppenheimer molecular dynamics trajectories. We will illustrate these capabilities via time-resolved Raman spectra computed during explicit, reactive molecular dynamics simulations of the shock compression of methane, benzene, tert-butylacetylene. Comparisons will be made with experimental results where possible.

Niklasson, Anders; Coe, Joshua; Cawkwell, Marc

2011-06-01

87

NASA Astrophysics Data System (ADS)

In this paper, a new particle image velocimetry (PIV)-based measurement method is proposed to obtain the high-resolution tide-induced Lagrangian residual current field in the laboratory. A long gravity wave was generated to simulate the tide in a narrow tank full of water laden with PIV particles. Consecutive charge-coupled device (CCD) images were recorded with the studied layer illuminated with a laser beam. Two images separated by one tidal period were processed by applying the pattern-matching algorithm to get the horizontal tide-induced Lagrangian residual current field. The results coincide with sporadic results from the traditional surface-float tracing method, but with much higher spatial resolution and accuracy. Furthermore, it is found that the direct acquisition of the Lagrangian residual current may reduce the error at least by one order compared with those acquisition methods that require the detailed information of the tidal cycle.

Wang, Tao; Jiang, Wensheng; Chen, Xu; Feng, Shizuo

2013-12-01

88

Invariants from classical field theory

We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.

Diaz, Rafael [Grupo de Fisica-Matematica, Universidad Experimental Politecnica de las Fuerzas Armadas, Caracas 1010 (Venezuela); Leal, Lorenzo [Centro de Fisica Teorica y Computacional, Universidad Central de Venezuela, Caracas 1041-A (Venezuela)

2008-06-15

89

Effective field theory of modified gravity with two scalar fields: Dark energy and dark matter

NASA Astrophysics Data System (ADS)

We present a framework for discussing the cosmology of dark energy and dark matter based on two scalar degrees of freedom. An effective field theory of cosmological perturbations is employed. A unitary gauge choice renders the dark energy field into the gravitational sector, for which we adopt a generic Lagrangian depending on three-dimensional geometrical scalar quantities arising in the Arnowitt-Deser-Misner decomposition. We add to this dark energy-associated gravitational sector a scalar field ? and its kinetic energy X as dark matter variables. Compared to the single-field case, we find that there are additional conditions to obey in order to keep the equations of motion for linear cosmological perturbations at second order. For such a second-order multifield theory, we derive conditions under which ghosts and Laplacian instabilities of the scalar and tensor perturbations are absent. We apply our general results to models with dark energy emerging in the framework of the Horndeski theory and dark matter described by a k-essence Lagrangian P(? ,X). We derive the effective coupling between such an imperfect-fluid dark matter and the gravitational sector under the quasistatic approximation on subhorizon scales. By considering the purely kinetic Lagrangian P(X) as a particular case, the formalism is verified to reproduce the gravitational coupling of a perfect-fluid dark matter.

Gergely, László Á.; Tsujikawa, Shinji

2014-03-01

90

Histories and observables in covariant field theory

NASA Astrophysics Data System (ADS)

Motivated by DeWitt's viewpoint of covariant field theory, we define a general notion of a non-local classical observable that applies to many physical Lagrangian systems (with bosonic and fermionic variables), by using methods that are now standard in algebraic geometry. We review the methods of local functional calculus, as they are presented by Beilinson and Drinfeld, and relate them to our construction. We partially explain the relation of these with Vinogradov's secondary calculus. The methods present here are all necessary to understand mathematically properly, and with simple notions, the full renormalization of the standard model, based on functional integral methods. Our approach is close in spirit to non-perturbative methods since we work with actual functions on spaces of fields, and not only formal power series. This article can be seen as an introduction to well-grounded classical physical mathematics, and as a good starting point to study quantum physical mathematics, which make frequent use of non-local functionals, like for example in the computation of Wilson's effective action. We finish by describing briefly a coordinate-free approach to the classical Batalin-Vilkovisky formalism for general gauge theories, in the language of homotopical geometry.

Paugam, Frédéric

2011-09-01

91

Resolving Witten's superstring field theory

NASA Astrophysics Data System (ADS)

We regulate Witten's open superstring field theory by replacing the picturechanging insertion at the midpoint with a contour integral of picture changing insertions over the half-string overlaps of the cubic vertex. The resulting product between string fields is non-associative, but we provide a solution to the A ? relations defining all higher vertices. The result is an explicit covariant superstring field theory which by construction satisfies the classical BV master equation.

Erler, Theodore; Konopka, Sebastian; Sachs, Ivo

2014-04-01

92

The matrix forms of local Lagrangian approach (LLA) are developed based on Lagrangian description for single-component in nonlinear, non-ideal chromatography. A local thermodynamic path (LTP) is designed based on essential physical principles, such as the Lagrangian description, the local equilibrium assumption and the thermodynamic state functions. With the LTP, the iteration equations of fully thermodynamic states on time sequence in the matrix forms are obtained with the Markov character. And the convergence, compatibility and stability of the LLA based on the LTP are discussed with some theoretical analysis and numerical experiments, and the stability condition of the LLA is given. The algorithm of the LLA in the vector form is shown as the computer program to simulate the elution profiles affected by a few of factors, space-distribution, axial diffusions, injection samples, etc. According to the LLA, the corresponding relationships are established between the trajectories of discrete time state and discrete time control vectors in the ergodic space. And a compendium algorithm of multistage decision problems concerning the optimal control of nonlinear, non-idea chromatography is given with Bellman's dynamic programming to find the optimal trajectories of state vector and control vector. The matrix forms of the LLA remove the gap between preparative chromatography theories and Markov decision processes or optimal control approaches based on discrete time states. PMID:18161316

Liang, Heng

2007-09-01

93

We study here, in two spatial dimensions, the effective Lagrangian of nonrelativistic charged fermions in an electromagnetic field. The fermionic integration is performed yielding a one-loop effective action that is evaluated using the inhomogeneity (derivative) expansion technique. The effective Lagrangian involves a Chern-Simons (CS) -like term with a coefficient that is a ``staircase'' function of B, the magnetic field. We

Prasanta K. Panigrahi; Rashmi Ray; B. Sakita

1990-01-01

94

NASA Astrophysics Data System (ADS)

The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self-contained and serves as a "first aid kit" before one ventures into the beautiful but bewildering landscape of Woronowicz's theory. First, we present an up-to-date account of the methods and definitions used in quantum gauge theories. Then, we highlight our new results. The present paper is by no means an exhaustive overview of this swiftly developing subject.

Mesref, L.

95

Galilean covariant Lagrangian models

NASA Astrophysics Data System (ADS)

We construct non-relativistic Lagrangian field models by enforcing Galilean covariance with a (4, 1) Minkowski manifold followed by a projection onto the (3, 1) Newtonian spacetime. We discuss scalar, Fermi and gauge fields, as well as interactions between these fields, preparing the stage for their quantization. We show that the Galilean covariant formalism provides an elegant construction of the Lagrangians which describe the electric and magnetic limits of Galilean electromagnetism. Similarly we obtain non-relativistic limits for the Proca field. Then we study Dirac Lagrangians and retrieve the Lévy-Leblond wave equations when the Fermi field interacts with an Abelian gauge field.

Santos, E. S.; de Montigny, M.; Khanna, F. C.; Santana, A. E.

2004-10-01

96

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

97

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

98

Equivalence of Hamiltonian and Lagrangian Path Integral Quantization

NASA Astrophysics Data System (ADS)

The HLE theorem is proven for effective Lagrangians with arbitrary interactions of scalars, fermions, massless and massive vector bosons. This theorem states that the correct Hamiltonian path intergral formalism is equivalent to the convenient Lagrangian path integral ansatz. In particular, this theorem is valid for effective gauge theories, which justifies Faddeev-Popov quantization of these theories. Specific attention is paid to effective interactions of massive vector fields, which can be embedded within gauge noninvariant theories or within spontaneously broken gauge theories. These different types of models are related to each other by the Stuckelberg formalism, which is reformulated within the Hamiltonian formalism. Effective Lagrangians with higher derivatives of the fields are also considered. The HLE theorem is even valid in this case because each effective higher-order Lagrangian can be reduced to a first-order one by applying the equations of motion to the effective interaction term. This thesis is essentially a combination of previous publications of the author.

Grosse-Knetter, Carsten

1993-11-01

99

Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect

We derive the lagrangian and transformation laws of the coupled Yang-Mills-matter-supergravity system for unextended n = 1 local supersymmetry. We study the super-Higgs effect and the normal Higgs effect of the Yang-Mills gauge group G. In the case of N chiral multiplets ``minimally'' coupled to supergravity, transforming according to some N-dimensional, generally reducible representation of G, we find a model-independent

E. Cremmer; Sergio Ferrara; L. Girardello; A. van Proeyen

1983-01-01

100

Effective field theory for inflation

The methods of effective field theory are used to study generic theories of inflation with a single inflaton field. For scalar modes, the leading corrections to the R correlation function are found to be purely of the k-inflation type. For tensor modes the leading corrections to the correlation function arise from terms in the action that are quadratic in the curvature, including a parity-violating term that makes the propagation of these modes depend on their helicity. These methods are also briefly applied to nongeneric theories of inflation with an extra shift symmetry, as in so-called ghost inflation.

Weinberg, Steven [Theory Group, Department of Physics, University of Texas, Austin, TX, 78712 (United States)

2008-06-15

101

Quantum field theory without divergences

It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to unmeasurable (and hence unphysical) quantities. This is because no physical quantity can be measured in a point, but in a region, the size of which is constrained by the resolution of measuring equipment. The incorporation of the resolution into the definition of quantum fields {phi}(x){yields}{phi}{sup (A)}(x) and appropriate change of Feynman rules results in finite values of the Green functions. The Euclidean {phi}{sup 4}-field theory is taken as an example.

Altaisky, M. V. [Joint Institute for Nuclear Research, Dubna, 141980 (Russian Federation); and Space Research Institute RAS, Profsoyuznaya 84/32, Moscow, 117997 (Russian Federation)

2010-06-15

102

Tail terms in gravitational radiation reaction via effective field theory

NASA Astrophysics Data System (ADS)

Gravitational radiation reaction affects the dynamics of gravitationally bound binary systems. Here we focus on the leading “tail” term which modifies binary dynamics at fourth post-Newtonian order, as first computed by Blanchet and Damour. We reproduce this result using effective field theory techniques in the framework of the Lagrangian formalism suitably extended to include dissipation effects. We recover the known logarithmic tail term, consistently with the recent interpretation of the logarithmic tail term in the mass parameter, as a renormalization group effect of the Bondi mass of the system.

Foffa, Stefano; Sturani, Riccardo

2013-02-01

103

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

104

Lagrangian description of warm plasmas

NASA Technical Reports Server (NTRS)

Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.

Kim, H.

1970-01-01

105

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

NASA Technical Reports Server (NTRS)

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Vandommelen, Leon L.; Cowley, Stephen J.

1989-01-01

106

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

107

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

108

Maxwell-like Lagrangians for higher spins

NASA Astrophysics Data System (ADS)

We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless fields produce single-particle actions, while whenever trace constraints can be dispensed with the resulting Lagrangians display the same reducible, multi-particle spectra as those emerging from the tensionless limit of free open-string field theory. For all explored options the corresponding kinetic operators take essentially the same form as in the spin-one, Maxwell case.

Campoleoni, Andrea; Francia, Dario

2013-03-01

109

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

110

Quantum Field Theory, Revised Edition

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

F. Mandl; G. Shaw

1994-01-01

111

National Technical Information Service (NTIS)

The parametric equations of KAM tori for a l degrees of freedom quasi integrable system are shown to be one point Schwinger functions of a suitable euclidean quantum field theory on the l dimensional torus. KAM theorem is equivalent to a ultraviolet stabi...

G. Gallavotti G. Gentile V. Mastropietro

1995-01-01

112

NASA Technical Reports Server (NTRS)

It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange multipliers). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel regularization. Some interesting applications to perturbation theory are also described.

Broucke, R.; Lass, H.

1975-01-01

113

We present an efficient general approach to first principles molecular dynamics simulations based on extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field optimization. The reduction of the optimization requirement reduces the computational cost to a minimum, but without causing any significant loss of accuracy or long-term energy drift. The optimization-free first principles molecular dynamics requires only one single diagonalization per time step, but is still able to provide trajectories at the same level of accuracy as “exact,” fully converged, Born-Oppenheimer molecular dynamics simulations. The optimization-free limit of extended Lagrangian Born-Oppenheimer molecular dynamics therefore represents an ideal starting point for robust and efficient first principles quantum mechanical molecular dynamics simulations.

Souvatzis, Petros, E-mail: petros.souvatsiz@fysik.uu.se [Department of Physics and Astronomy, Division of Materials Theory, Uppsala University, Box 516, SE-75120, Uppsala (Sweden)] [Department of Physics and Astronomy, Division of Materials Theory, Uppsala University, Box 516, SE-75120, Uppsala (Sweden); Niklasson, Anders M. N., E-mail: amn@lanl.gov [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)] [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

2013-12-07

114

Strongly coupled quantum field theory

I analyze numerically a two-dimensional {lambda}{phi}{sup 4} theory showing that in the limit of a strong coupling {lambda}{yields}{infinity} just the homogeneous solutions for time evolution are relevant in agreement with the duality principle in perturbation theory as presented in [M. Frasca, Phys. Rev. A 58, 3439 (1998)], being negligible the contribution of the spatial varying parts of the dynamical equations. A consequence is that the Green function method works for this nonlinear problem in the large coupling limit as in a linear theory. A numerical proof is given for this. With these results at hand, I built a strongly coupled quantum field theory for a {lambda}{phi}{sup 4} interacting field computing the first order correction to the generating functional. Mass spectrum of the theory is obtained turning out to be that of a harmonic oscillator with no dependence on the dimensionality of space-time. The agreement with the Lehmann-Kaellen representation of the perturbation series is then shown at the first order.

Frasca, Marco

2006-01-15

115

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

116

NASA Astrophysics Data System (ADS)

The breathing-mode isoscalar giant monopole resonance (GMR) is investigated using the generator coordinate method within the relativistic mean-field (RMF) theory. Employing the Lagrangian models of the nonlinear-? model (NL?), the scalar-vector interaction model (SVI) and the ?-? coupling model (SIGO), we show that each Lagrangian model exhibits a distinctly different GMR response. Consequently, Lagrangian models yield a different value of the GMR energy for a given value of the nuclear matter incompressibility K. It is shown that this effect arises largely from a different value of the surface incompressibility K inherent to each Lagrangian model, thus giving rise to the ratio K/K which depends upon the Lagrangian model used. This is attributed to a difference in the density dependence of the meson masses and hence to the density dependence of the nuclear interaction amongst various Lagrangian models. The sensitivity of the GMR energy to the Lagrangian model used and thus emergence of a multitude of GMR energies for a given value of K renders the method of extracting K on the basis of interpolation amongst forces as inappropriate. As a remedy, the need to ‘calibrate’ the density dependence of the nuclear interaction in the RMF theory is proposed.

Sharma, M. M.

2009-01-01

117

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

118

Density dependent hadron field theory

NASA Astrophysics Data System (ADS)

A fully covariant approach to a density dependent hadron field theory is presented. The relation between in-medium NN interactions and field-theoretical meson-nucleon vertices is discussed. The medium dependence of nuclear interactions is described by a functional dependence of the meson-nucleon vertices on the baryon field operators. As a consequence, the Euler-Lagrange equations lead to baryon rearrangement self-energies which are not obtained when only a parametric dependence of the vertices on the density is assumed. It is shown that the approach is energy-momentum conserving and thermodynamically consistent. Solutions of the field equations are studied in the mean-field approximation. Descriptions of the medium dependence in terms of the baryon scalar and vector density are investigated. Applications to infinite nuclear matter and finite nuclei are discussed. Density dependent coupling constants obtained from Dirac-Brueckner calculations with the Bonn NN potentials are used. Results from Hartree calculations for energy spectra, binding energies, and charge density distributions of 16O, 40,48Ca, and 208Pb are presented. Comparisons to data strongly support the importance of rearrangement in a relativistic density dependent field theory. Most striking is the simultaneous improvement of charge radii, charge densities, and binding energies. The results indicate the appearance of a new ``Coester line'' in the nuclear matter equation of state.

Fuchs, C.; Lenske, H.; Wolter, H. H.

1995-12-01

119

String field theory-inspired algebraic structures in gauge theories

We consider gauge theories in a string field theory-inspired formalism. The constructed algebraic operations lead, in particular, to homotopy algebras of the related Batalin-Vilkovisky theories. We discuss an invariant description of the gauge fixing procedure and special algebraic features of gauge theories coupled to matter fields.

Zeitlin, Anton M. [Department of Mathematics, Yale University, 442 Dunham Lab., 10 Hillhouse Ave., New Haven, Connecticut 06511 (United States)

2009-06-15

120

Statistical predictions from anarchic field theory landscapes

Consistent coupling of effective field theories with a quantum theory of gravity appears to require bounds on the rank of the gauge group and the amount of matter. We consider landscapes of field theories subject to such to boundedness constraints. We argue that appropriately “coarse-grained” aspects of the randomly chosen field theory in such landscapes, such as the fraction of

Vijay Balasubramanian; Jan de Boer; Asad Naqvi

2010-01-01

121

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

122

Variational methods for field theories

Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.

Ben-Menahem, S.

1986-09-01

123

Topics in Perturbative Field Theory.

NASA Astrophysics Data System (ADS)

This thesis discusses several results in perturbative field theory. The first two sections present a calculation of the order (alpha)(,s)('2) corrections to the event shape in e('+)e('-) annihilation into hadrons. A technique for the calculation of Feynman diagrams based upon a generalization of the multipole expansion of a potential is discussed in the third section. Computer programs which can be used evaluate the traces which arise in the evaluation of Feynman diagrams are described in an Appendix.

Terrano, Anthony Emerson

124

Topics in Perturbative Field Theory

This thesis discusses several results in perturbative field theory. The first two sections present a calculation of the order (alpha)(,s)('2) corrections to the event shape in e('+)e('-) annihilation into hadrons. A technique for the calculation of Feynman diagrams based upon a generalization of the multipole expansion of a potential is discussed in the third section. Computer programs which can be

Anthony Emerson Terrano

1981-01-01

125

Hamiltonian field theory of ferrohydrodynamics.

A Hamiltonian field theory of ferrohydrodynamics is derived, with dissipation included by use of a Rayleigh dissipation function. It is shown that kinematic assumptions on the behavior of magnetization under displacements of a volume element of fluid leave a certain freedom in the construction of dynamical equations describing the time-dependence of mass density, flow velocity, entropy density, magnetization, and spin density. The convective behavior of magnetization may be characterized by two dimensionless coefficients. PMID:22010729

Felderhof, B U; Sokolov, V V; Éminov, P A

2011-10-14

126

Symmetries and strings in field theory and gravity

NASA Astrophysics Data System (ADS)

We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of Zp gauge theories shows that they are associated with an emergent Zp 1-form (Kalb-Ramond) gauge symmetry. This understanding leads us to uncover new observables and new phenomena in nonlinear ? models. It also allows us to expand on Polchinski’s classification of cosmic strings. We argue that in models of quantum gravity, there are no global symmetries, all continuous gauge symmetries are compact, and all charges allowed by Dirac quantization are present in the spectrum. These conjectures are not new, but we present them from a streamlined and unified perspective. Finally, our discussion about string charges and symmetries leads to a more physical and more complete understanding of recently found consistency conditions of supergravity.

Banks, Tom; Seiberg, Nathan

2011-04-01

127

From operator algebras to superconformal field theory

We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.

Kawahigashi, Yasuyuki [Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914 (Japan)

2010-01-15

128

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

129

Quantum Field Theory of Interacting Tachyons

A quantum field theory of spin-0 particles traveling with speeds greater than that of light has been constructed. The theory constructed here is explicitly Lorentz-invariant; and the quanta of the field obey Bose statistics. Formalism developed for the free field has been extended to the case of interaction of these particles with nucleons. A new feature of theory is the

J. Dhar; E. C. G. Sudarshan

1968-01-01

130

Noncommutative Dipole Field Theories And Unitarity

We extend the argument of Gomis and Mehen for violation of unitarity in field theories with space-time noncommutativity to dipole field theories. In dipole field theories with a timelike dipole vector, we present 1-loop amplitudes that violate the optical theorem. A quantum mechanical system with nonlocal potential of finite extent in time also shows violation of unitarity.

Chiou, Dah-Wei; Ganor, Ori J.

2003-10-24

131

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

132

Group field theory with noncommutative metric variables.

We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action. PMID:21231377

Baratin, Aristide; Oriti, Daniele

2010-11-26

133

NASA Astrophysics Data System (ADS)

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.JHEPFG1029-8479 06 (2008) 105.10.1088/1126-6708/2008/06/105] 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.JHEPFG1029-8479 08 (2008) 014.10.1088/1126-6708/2008/08/014] 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; Samsonov, Igor; Sorokin, Dmitri; Tonin, Mario

2009-10-01

134

On nonperturbative solutions of superstring field theory

NASA Astrophysics Data System (ADS)

Nonperturbative solutions to the nonlinear field equations in the NS sector of cubic as well as nonpolynomial superstring field theory can be obtained from a linear equation which includes a “spectral” parameter ? and a coboundary operator Q( ?). We borrow a simple ansatz from the dressing method (for generating solitons in integrable field theories) and show that classical superstring fields can be constructed from any string field T subject merely to Q( ?) T=0. Following the decay of the non-BPS D9 brane in IIA theory and shifting the background to the tachyon vacuum, we repeat the arguments in vacuum superstring field theory and outline how to compute classical solutions explicitly.

Kling, Alexander; Lechtenfeld, Olaf; Popov, Alexander D.; Uhlmann, Sebastian

2003-01-01

135

Dual of the Janus solution: An interface conformal field theory

We propose and study a specific gauge theory dual of the smooth, nonsupersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in Bak et al. [J. High Energy Phys. 05 (2003) 072]. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L{sup '} which is the fourth descendent of the primary TrX{sup {l_brace}}{sup I}X{sup J{r_brace}} and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of g{sub YM}{sup 2}, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value

Clark, A.B.; Karch, A. [Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States); Freedman, D.Z. [Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Schnabl, M. [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

2005-03-15

136

Variant of the bimetric theory of gravitation. II. Energy-momentum tensor of the gravitational field

Starting from the invariance of action relative to coordinate transformations, differential conservation laws are established\\u000a in the bimetric theory of gravitation with a Lagrangian that is quadratic with respect to “intensities.” Explicit expressions\\u000a are found for the canonical and metric energymomentum tensors of the gravitational field, as well as for the tensor analog\\u000a of the Landau-Lifshitz pseudotensor.

R. M. Avagyan; A. H. Yeranyan

2000-01-01

137

Quantum Field Theory and Computational Paradigms

We introduce the basic theory of quantization of radiation field in quantum physics and explain how it relates to the theory of recursive functions in computer science. We outline the basic differences between quantum mechanics (QM) and quantum field theory (QFT) and explain why QFT is better suited for a computational paradigm - based on algorithmic requirement, countably infinite degrees

E. V. Krishnamurthy; Vikram Krishnamurthy

2001-01-01

138

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

139

Lagrangian form of Schrödinger equation

NASA Astrophysics Data System (ADS)

Lagrangian formulation of quantum mechanical Schrödinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein-Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schrödinger equation.

Arsenovi?, D.; Buri?, N.; Davidovi?, D. M.; Prvanovi?, S.

2014-06-01

140

Gauge fields and fermions in tachyon effective field theories

In this paper we incorporate gauge fields into the tachyon field theory models for unstable D-branes in bosonic and in type-II string theories. The chosen couplings yield massless gauge fields and an infinite set of equally spaced massive gauge fields on codimension one branes. A lack of a continuum spectrum is taken as evidence that the stable tachyon vacuum does

Joseph A. Minahan; Barton Zwiebach

2001-01-01

141

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

142

Homotopy Classification of Bosonic String Field Theory

NASA Astrophysics Data System (ADS)

We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.

Münster, Korbinian; Sachs, Ivo

2014-05-01

143

Supersymmetric field theories and generalized cohomology

NASA Astrophysics Data System (ADS)

lt is conjectured that the tmf spectrum, constructed by Hopkins and Miller, can be described in terms of 'spaces' of conformal field theories. In this dissertation, spaces of field theories are constructed as classifying spaces of categories whose objects are certain types of field theories. These categories have symmetric monoidal structures and their sets of components turn out to form groups. Therefore; by work of Segal in the 70s, their classifying spaces are infinite loop spaces, hence define generalized cohomology theories. There are the following two examples. (i) A category SEFTn is constructed for each n ? Z whose objects are Stolz-Teichner's (1|1)-dimensional super Euclidean field theories of degree n. It is proved that the classifying space | SEFTn | represents the degree n K or KO cohomology. Whether we have K or KO depends on the coefficients of the field theories. (ii) There are (2|1)-dimensional field theories, called 'annular field theories', defined using supergeometric versions of circles and annuli only. Using these field theories as objects, a category AFTn is constructed for each n ? Z . It is proved that the classifying space | AFTn | represents the degree n elliptic cohomology associated with the Tate curve. Detailed definitions of the field theories are given.

Cheung, Pok Man

144

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. [Department of Physics, University of California, Berkeley, California 94720, USA and Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)

2007-01-15

145

On revolutionizing quantum field theory with Tomita's modular theory

In the book of Haag [Local Quantum Physics (Springer Verlag, Berlin, 1992)] about local quantum field theory the main results are obtained by the older methods of C*- and W*-algebra theory. A great advance, especially in the theory of W*-algebras, is due to Tomita's discovery of the theory of modular Hilbert algebras [Quasi-standard von Neumann algebras, Preprint (1967)]. Because of

H. J. Borchers

2000-01-01

146

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

147

Noncommutative scalar field theories, solitons and superalgebra

NASA Astrophysics Data System (ADS)

This dissertation presents perturbative and nonperturbative aspects of noncommutative (NC) field theories, as well as superalgebras in NC field theory and higher dimensional theories. In particular, the perturbative structures of the NC Wess-Zumino model are investigated in detail, as well as the deformed superalgebra relations of the model. NC solitons in scalar field theory are quantized and quantum corrections to the energy are calculated, where UV-IR divergences are found similar to those in the perturbative theory. Kostant equations in higher dimensions are constructed with differential form representations, in which the solutions are also expressed.

Xiong, Xiaozhen

148

A field theory of consciousness.

This article summarizes a variety of current as well as previous research in support of a new theory of consciousness. Evidence has been steadily accumulating that information about a stimulus complex is distributed to many neuronal populations dispersed throughout the brain and is represented by the departure from randomness of the temporal pattern of neural discharges within these large ensembles. Zero phase lag synchronization occurs between discharges of neurons in different brain regions and is enhanced by presentation of stimuli. This evidence further suggests that spatiotemporal patterns of coherence, which have been identified by spatial principal component analysis, may encode a multidimensional representation of a present or past event. How such distributed information is integrated into a holistic precept constitutes the binding problem. How a precept defined by a spatial distribution of nonrandomness can be subjectively experienced constitutes the problem of consciousness. Explanations based on a discrete connectionistic network cannot be reconciled with the relevant facts. Evidence is presented herein of invariant features of brain electrical activity found to change reversibly with loss and return of consciousness in a study of 176 patients anesthetized during surgical procedures. A review of relevant research areas, as well as the anesthesia data, leads to a postulation that consciousness is a property of quantum-like processes, within a brain field resonating within a core of structures, which may be the neural substrate of consciousness. This core includes regions of the prefrontal cortex, the frontal cortex, the pre- and paracentral cortex, thalamus, limbic system, and basal ganglia. PMID:11414714

John, E R

2001-06-01

149

In this paper, we develop the sufficient conditions for the existence of local and global saddle points of two classes of augmented Lagrangian functions for nonconvex optimization problem with both equality and inequality constraints, which improve the corresponding results in available papers. The main feature of our sufficient condition for the existence of global saddle points is that we do not need the uniqueness of the optimal solution. Furthermore, we show that the existence of global saddle points is a necessary and sufficient condition for the exact penalty representation in the framework of augmented Lagrangians. Based on these, we convert a class of generalized semi-infinite programming problems into standard semi-infinite programming problems via augmented Lagrangians. Some new first-order optimality conditions are also discussed.

Wang Changyu [Qufu Normal University, Institute of Operations Research (China)], E-mail: wcy0537@126.com; Zhou Jinchuan [Beijing Jiaotong University, Department of Mathematics, School of Science (China)], E-mail: jinchuanzhou@yahoo.com.cn; Xu Xiuhua [Zibo Experimental High School (China)], E-mail: xxh123456@163.com

2009-06-15

150

Quantum Field Theory and Elementary Particles.

National Technical Information Service (NTIS)

Contents: Mathematical theory of Pade approximants; Application of Pade approximants to renormalisable fields; Other applications of Pade approximants; Calculation of higher-order matrix elements; and Singular potentials and non-renormalisable fields.

S. R. Chisholm

1968-01-01

151

On Lagrangian and vortex-surface fields in Taylor-Green and Kida-Pelz flows

A methodology is developed for constructing smooth scalar fields phi for Taylor-Green and Kida-Pelz velocity fields that, at t=0, satisfy phi.?phi=0. We refer to such fields as vortex-surface fields. Iso-surfaces of phi then define vortex surfaces. Given the vorticity, our definition of a vortex-surface field is shown to admit nonuniqueness, and this is resolved numerically using an optimization approach. Equations

Dale Pullin; Yue Yang

2010-01-01

152

Functional Approach to Derivative Expansion of the Effective Lagrangian.

National Technical Information Service (NTIS)

A new functional method is given for calculating higher derivatives terms in the one-loop effective Lagrangian for multi-component scalar field theories. The general results obtained are illustrated with explicit calculations for the O(n)-invariant (phi s...

J. A. Zuk

1985-01-01

153

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

154

Axiomatic Quantum Field Theory in Curved Spacetime

NASA Astrophysics Data System (ADS)

The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincaré invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is constructed in a local and covariant manner from the spacetime metric and other background structure, such as time and space orientations), a microlocal spectrum condition, an “associativity” condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.

Hollands, Stefan; Wald, Robert M.

2010-01-01

155

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

156

Noncommutative field theory and Lorentz violation.

The role of Lorentz symmetry in noncommutative field theory is considered. Any realistic noncommutative theory is found to be physically equivalent to a subset of a general Lorentz-violating standard-model extension involving ordinary fields. Some theoretical consequences are discussed. Existing experiments bound the scale of the noncommutativity parameter to (10 TeV)(-2). PMID:11580640

Carroll, S M; Harvey, J A; Kostelecký, V A; Lane, C D; Okamoto, T

2001-10-01

157

Noncommutative Field Theory and Lorentz Violation

The role of Lorentz symmetry in noncommutative field theory is considered. Any realistic noncommutative theory is found to be physically equivalent to a subset of a general Lorentz-violating standard-model extension involving ordinary fields. Some theoretical consequences are discussed. Existing experiments bound the scale of the noncommutativity parameter to (10 TeV){sup -2} .

Carroll, Sean M.; Harvey, Jeffrey A.; Kostelecky, V. Alan; Lane, Charles D.; Okamoto, Takemi

2001-10-01

158

KAM Theorem and Quantum Field Theory

NASA Astrophysics Data System (ADS)

We give a new proof of the KAM theorem for analytic Hamiltonians. The proof is inspired by a quantum field theory formulation of the problem and is based on a renormalization group argument treating the small denominators inductively scale by scale. The crucial cancellations of resonances are shown to follow from the Ward identities expressing the translation invariance of the corresponding field theory.

Bricmont, Jean; Gaw?dzki, Krzysztof; Kupiainen, Antti

159

Tachyon Matter in Boundary String Field Theory

We analyse the classical decay process of unstable D-branes in superstring theory using the boundary string field theory (BSFT) action. We show that the solutions of the equations of motion for the tachyon field asymptotically approach to T = x0 and the pressure rapidly falls off at late time producing the tachyon matter irrespective of the initial condition. We also

Shigeki Sugimoto; Seiji Terashima

2002-01-01

160

Mirror Manifolds And Topological Field Theory

These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by twisting $N=2$ sigma models. This is mainly a review of old results, except for the discussion in \\\\S7 of certain facts that may be

Edward Witten

1991-01-01

161

Monte Carlo approaches to effective field theories.

National Technical Information Service (NTIS)

In this paper, we explore the application of continuum Monte Carlo methods to effective field theory models. Effective field theories, in this context, are those in which a Fock space decomposition of the state is useful. These problems arise both in nucl...

J. Carlson K. E. Schmidt

1991-01-01

162

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

163

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

164

Geometric engineering of quantum field theories

Using the recent advances in our understanding of non-perturbative aspects of type 11 strings we show how non-trivial exact results for N = 2 quantum field theories can be reduced to T-dualities of string theory. This is done by constructing a local geometric realization of quantum field theories together with a local application of mirror symmetry. This construction is not

Sheldon Katz; Albrecht Klemm; Cumrun Vafa

1997-01-01

165

Quantum field theory on noncommutative spaces

A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV\\/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study

Richard J. Szabo

2003-01-01

166

Quantum field theory on noncommutative spaces

A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl–Wigner correspondence, noncommutative Feynman diagrams, UV\\/IR mixing, noncommutative Yang–Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study

Richard J. Szabo

2003-01-01

167

Geometric Engineering of Quantum Field Theories

this paper is whether we can derive non-trivialfield theory results directly as a consequence of the recently acquired deeper understandingof string theory dynamics, rather than as a result of a consequence of a duality conjecture.If so we can claim to understand non-trivial results in field theory simply based on theexistence of string theory and its established properties! As we shall

Sheldon Katz; Albrecht Klemm; Cumrun Vafa

1996-01-01

168

MEDSLIK-II, a Lagrangian marine surface 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 surface oil slick numerical model and rewrites 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 particle 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, the so-called MEDSLIK-II, based on its precursor MEDSLIK (Lardner et al., 1998, 2006; Zodiatis et al., 2008a). Part 2 of this paper describes the applications of the model 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.; Lardner, R.

2013-11-01

169

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

170

Abelian Gauge Theories with Tensor Gauge Fields.

National Technical Information Service (NTIS)

Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell elect...

E. Kapuscik

1984-01-01

171

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

172

Euclidean quantum field theory: Curved spacetimes and gauge fields

This thesis presents a new formulation of quantum field theory (QFT) on curved spacetimes, with definite advantages over previous formulations, and an introduction to the millennium prize problem on four-dimensional gauge theory. Our constructions are completely rigorous, making QFT on curved spacetimes into a subfield of mathematics, and we achieve the first analytic control over nonperturbative aspects of interacting theories

William Gordon Ritter

2007-01-01

173

Field theory models for tachyon and gauge field string dynamics

In hep-th\\/0008227, the unstable lump solution of phi3 theory was shown to have a spectrum governed by the solvable Schroedinger equation with the ell = 3 reflectionless potential and was used as a model for tachyon condensation in string theory. In this paper we study in detail an ellrightarrowinfty scalar field theory model whose lump solution mimics remarkably the string

Joseph A. Minahan; Barton Zwiebach

2000-01-01

174

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

175

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

176

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

177

Theory of Geomagnetic Field Reversals.

National Technical Information Service (NTIS)

It is shown that the strange attractor in phase space of the Rikitake two-disc dynamo is supressed by weak, if any, external magnetic field. Reversals of the external field causes the reversals of the dynamo field. Extension of the result obtained to geom...

P. I. Fomin L. V. Yurevich

1983-01-01

178

Quantum Field Theory with Varying Couplings

NASA Astrophysics Data System (ADS)

A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific choice of the coupling's profile for any finite-order perturbative expansion. For one of these cases, some tree and one-loop diagrams are calculated. This is an example of a theory where violation of Lorentz symmetry is not enhanced at the quantum level. We draw some consequences for the renormalization properties of certain classes of fractional field theories.

Calcagni, Gianluca; Nardelli, Giuseppe

2014-01-01

179

NASA Astrophysics Data System (ADS)

In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (?, ??)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length (\\triangle Xi)min = \\hbar ? {D? +? '}, \\forall i\\in \\{1, 2, ..., D\\}. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of ?? = 2? up to the first-order over ?. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee-Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot-Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19 m. The relationship between magnetostatics with a minimal length and the Gaete-Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor.45, 065401 (2012)] is investigated.

Moayedi, S. K.; Setare, M. R.; Khosropour, B.

2013-12-01

180

Asymptotic dynamics in quantum field theory

NASA Astrophysics Data System (ADS)

A crucial element of scattering theory and the LSZ reduction formula is the assumption that the coupling vanishes at large times. This is known not to hold for the theories of the Standard Model and in general such asymptotic dynamics is not well understood. We give a description of asymptotic dynamics in field theories which incorporates the important features of weak convergence and physical boundary conditions. Applications to theories with three and four point interactions are presented and the results are shown to be completely consistent with the results of perturbation theory.

Horan, Robin; Lavelle, Martin; McMullan, David

2000-07-01

181

An Introduction to Quantum Field Theory

NASA Astrophysics Data System (ADS)

Part I. Scalar Fields: 1. Classical fields and symmetries; 2. Canonical quantization; 3. Path integrals, perturbation theory and Feynman rules; 4. Scattering and cross sections for scalar fields; Part II. Fields with Spin: 5. Spinors, vectors and gauge invariance; 6. Spin and canonical quantization; 7. Path integrals for fermions and gauge fields; 8. Gauge theories at lowest order; Part III. Renormalization: 9. Loops, regularization and unitarity; 10. Introduction to renormalization; 11. Renormalization and unitarity of gauge theories; Part IV. The Nature of Perturbative Cross Sections: 12. Perturbative corrections and the infrared problem; 13. Analytic structure and infrared finiteness; 14. Factorization and evolution in high energy scattering; 15. Epilogue: bound states and the limitations of perturbation theory; Appendices; References; Index.

Sterman, George

1993-08-01

182

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

183

The theory of the Galactic magnetic field

NASA Technical Reports Server (NTRS)

The paper discusses the role of the magnetic field in determining the large scale structure and dynamics of the interstellar medium. It then discusses the origin and maintenance of the Galactic field. The two major competing theories are that the field is primordial and connected to an intergalactic field or that the field is removed from and regenerated within the Galaxy. Finally, cosmic ray acceleration and confinement in the interstellar medium are discussed.

Zweibel, Ellen G.

1987-01-01

184

Noncommutative field theory from twisted Fock space

We construct a quantum field theory in noncommutative space time by twisting the algebra of quantum operators (especially, creation and annihilation operators) of the corresponding quantum field theory in commutative space time. The twisted Fock space and S-matrix consistent with this algebra have been constructed. The resultant S-matrix is consistent with that of Filk [Tomas Filk, Phys. Lett. B 376, 53 (1996).]. We find from this formulation that the spin-statistics relation is not violated in the canonical noncommutative field theories.

Bu, Jong-Geon; Kim, Hyeong-Chan; Lee, Youngone; Vac, Chang Hyon; Yee, Jae Hyung [Department of Physics, Yonsei University, Seoul (Korea, Republic of)

2006-06-15

185

Time independent mean-field theory

The physical and theoretical motivations for the time-dependent mean-field theory are presented, and the successes and limitations of the time-dependent Hartree-Fock initial-vaue problem are reviewed. New theoretical developments are described in the treatment of two-body correlations and the formulation of a quantum mean-field theory of large-amplitude collective motion and tunneling decay. Finally, the mean-field theory is used to obtain new insights into the phenomenon of pion condensation in finite nuclei. 18 figures.

Negele, J.W.

1980-02-01

186

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

187

Scaling Limits of Integrable Quantum Field Theories

NASA Astrophysics Data System (ADS)

Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is shown that massless scaling limit theories exist, and decompose into (twisted) tensor products of chiral, translation-dilation covariant field theories. On the subspace which is generated from the vacuum by the observables localized in finite light ray intervals, this symmetry can be extended to the Möbius group. The structure of the interval-localized algebras in the chiral models is discussed in two explicit examples.

Bostelmann, Henning; Lechner, Gandalf; Morsella, Gerardo

188

Moduli spaces and topological quantum field theories

We show how to construct a topological quantum field theory which corresponds to a given moduli space. This method is applied to several cases. In particular we discuss the moduli space of flat gauge connections over a Riemann surface which is related to the phase space of the Chern-Simons theory. The observables of these theories are derived. Geometrical properties are invoked to prove that the global invariants are not trivial. 14 refs., 3 tabs.

Sonnenschein, J.

1989-07-01

189

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

190

Selected Topics in Computational Quantum Field Theory.

National Technical Information Service (NTIS)

The main mathematical structures of the quantum field theory on the lattice; fractal lattices; the problem of the continual limit and the method of finite element for a solution of the operator equations of the quantum theory are considered. 25 refs. (Ato...

1985-01-01

191

Pion masses in quasiconformal gauge field theories

We study modifications to Weinberg-like sum rules in quasiconformal gauge field theories. Beyond the two Weinberg sum rules and the oblique S parameter, we study the pion mass and the X parameter. Especially, we evaluate the pion mass for walking technicolor theories, in particular, minimal walking technicolor, and find contributions of the order of up to several hundred GeV.

Dietrich, Dennis D.; Jaervinen, Matti [Center for High Energy Physics, University of Southern Denmark, Odense (Denmark)

2009-03-01

192

Quantum Mechanical Approximations in Quantum Field Theory.

National Technical Information Service (NTIS)

Some cooperative, coherent effects in quantum field theory, such as spontaneous symmetry violation, bound states, and entrapment of various excitations, can be exposed only by approximation procedures which do not rely on analyticity or regularity in the ...

R. Jackiw

1975-01-01

193

General Relativity Invariance and String Field Theory.

National Technical Information Service (NTIS)

The general covariance principle in the string field theory is considered. The algebraic properties of the string Lie derivative are discussed. The string vielbein and spin connection are introduced and an action invariant under general co-ordinate transf...

I. Y. Aref'eva I. V. Volovich

1987-01-01

194

Operatorial Methods in Noncommutative Field Theory

We review the operatorial quantization of noncommutative field theory, with emphasis on the fundamentally bilocal nature of the degrees of freedom. Interactions and IR/UV mixing are discussed from this point of view.

Acatrinei, Ciprian [Smoluchowski Institute of Physics, Jagellonian University Reymonta 4, Cracow (Poland)

2007-11-14

195

Mathematical Structures in Perturbation Quantum Field Theory

NASA Astrophysics Data System (ADS)

A brief overview is given of some of the mathematical structures underlying perturbation quantum field theory and renormalization, which may be relevant to the understanding of the small structure of space-time.

Rosenbaum, M.

2006-08-01

196

The zero-bin and mode factorization in quantum field theory

NASA Astrophysics Data System (ADS)

We study a Lagrangian formalism that avoids double counting in effective field theories where distinct fields are used to describe different infrared momentum regions for the same particle. The formalism leads to extra subtractions in certain diagrams and to a new way of thinking about factorization of modes in quantum field theory. In nonrelativistic field theories, the subtractions remove unphysical pinch singularities in box-type diagrams, and give a derivation of the known pullup mechanism between soft and ultrasoft fields which is required by the renormalization group evolution. In a field theory for energetic particles, the soft-collinear effective theory (SCET), the subtractions allow the theory to be defined with different infrared and ultraviolet regulators, remove double counting between soft, ultrasoft, and collinear modes, and give results which reproduce the infrared divergences of the full theory. Our analysis shows that convolution divergences in factorization formulas occur due to an overlap of momentum regions. We propose a method that avoids this double counting, which helps to resolve a long-standing puzzle with singularities in collinear factorization in QCD. The analysis gives evidence for a factorization in rapidity space in exclusive decays.

Manohar, Aneesh V.; Stewart, Iain W.

2007-10-01

197

Conformal field theory of twisted vertex operators

The Z2-twisted bosonic conformal field theory associated with a d-dimensional momentum lattice Lambda is constructed explicitly. A complete system of vertex operators (conformal fields) which describes this theory on the Riemann sphere is given and is demonstrated to form a mutually local set when d is a multiple of 8, Lambda is even, and &surd;2Lambda* is also even. (This last

L. Dolan; P. Goddard; P. Montague

1990-01-01

198

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

199

Effective Lagrangians for the string model of Bluhm, Dolan, and Goddard. I. The bosonic sector

We compute all the massless bosonic three-point and four-point tree amplitudes for the string model of Bluhm, Dolan, and Goddard. These amplitudes are then used to construct the bosonic effective Lagrangians that describe the dynamics of the theory at low energy. These effective Lagrangians are exact up to the quartic interaction terms in field variables, and are significantly different from those for the four-dimensional heterotic string model.

Chen, M. (Department of Physics, National Central University, Chung-Li, Taiwan 32054, Republic of China (CN)); Yeung, W.B. (Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China)

1989-08-15

200

Codimension two lump solutions in string field theory and tachyonic theories

We present some solutions for lumps in two dimensions in level-expanded string field theory, as well as in two tachyonic theories: pure tachyonic string field theory and pure $\\\\phi^3$ theory. Much easier to handle, these theories might be used to help understanding solitonic features of string field theory. We compare lump solutions between these theories and we discuss some convergence

Nicolas Moeller

2000-01-01

201

Viscosity, Black Holes, and Quantum Field Theory

NASA Astrophysics Data System (ADS)

We review recent progress in applying the AdS/CFT correspondence to finite-temperature field theory. In particular, we show how the hydrodynamic behavior of field theory is reflected in the low-momentum limit of correlation functions computed through a real-time AdS/CFT prescription, which we formulate. We also show how the hydrodynamic modes in field theory correspond to the low-lying quasi-normal modes of the AdS black p-brane metric. We provide proof of the universality of the viscosity/entropy ratio within a class of theories with gravity duals and formulate a viscosity bound conjecture. Possible implications for real systems are mentioned.

Son, Dam T.; Starinets, Andrei O.

2007-11-01

202

"Quantum Field Theory and QCD"

This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.

Jaffe, Arthur M.

2006-02-25

203

Noncommutative Geometry in M-Theory and Conformal Field Theory

In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.

Morariu, Bogdan

1999-05-01

204

Folding defect affine Toda field theories

NASA Astrophysics Data System (ADS)

A folding process is applied to fused a_r^{(1)} defects to construct defects for the non-simply laced affine Toda field theories of c_n^{(1)}, d_n^{(2)} and a_{2n}^{(2)} at the classical level. Support for the hypothesis that these defects are integrable in the folded theories is given by the demonstration that energy and momentum are conserved. Further support is provided by the observation that transmitted solitons retain their form.

Robertson, Craig

2014-05-01

205

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

206

Effective Field Theory and Precision Electroweak Measurements

NASA Astrophysics Data System (ADS)

The first part of these lectures provides a brief introduction to the concepts and techniques of effective field theory. The second part reviews precision electroweak constraints using effective theory methods. Several simple extensions of the Standard Model are considered as illustrations. The appendix contains some new results on the one-loop contributions of electroweak triplet scalars to the T parameter and contains a discussion of decoupling in that case.

Skiba, Witold

2011-03-01

207

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

208

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

209

Magnetic monopoles in field theory and cosmology.

The existence of magnetic monopoles is predicted by many theories of particle physics beyond the standard model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic monopoles in quantum field theory and discuss their implications for particle physics and cosmology. I also highlight their differences and similarities with monopoles found in frustrated magnetic systems. PMID:23166376

Rajantie, Arttu

2012-12-28

210

Stretched strings in noncommutative field theory

Motivated by recent discussions of IR-UV mixing in noncommutative field theories, we perform a detailed analysis of the nonplanar amplitudes of the bosonic open string in the presence of an external B field at the one-loop level. We carefully isolate, at the string theory level, the contribution which is responsible for the IR-UV behavior in the field theory limit. We show that it is a pure open string effect by deriving it from the factorization of the one-loop amplitude into the disk amplitudes of intermediate open string insertions. We suggest that it is natural to understand IR-UV mixing as the creation of intermediate ''stretched strings.'' (c) 2000 The American Physical Society.

Liu, Hong [New High Energy Theory Center, Rutgers University, 126 Frelinghuysen Road, Piscataway, New Jersey 08854 (United States)] [New High Energy Theory Center, Rutgers University, 126 Frelinghuysen Road, Piscataway, New Jersey 08854 (United States); Michelson, Jeremy [New High Energy Theory Center, Rutgers University, 126 Frelinghuysen Road, Piscataway, New Jersey 08854 (United States)] [New High Energy Theory Center, Rutgers University, 126 Frelinghuysen Road, Piscataway, New Jersey 08854 (United States)

2000-09-15

211

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

212

Conformal field theories in fractional dimensions.

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. PMID:24765941

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

2014-04-11

213

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

214

Quantum Field Theory and Computational Paradigms

NASA Astrophysics Data System (ADS)

We introduce the basic theory of quantization of radiation field in quantum physics and explain how it relates to the theory of recursive functions in computer science. We outline the basic differences between quantum mechanics (QM) and quantum field theory (QFT) and explain why QFT is better suited for a computational paradigm - based on algorithmic requirement, countably infinite degrees of freedom and the creation of macroscopic output objects. The quanta of the radiation field correspond to the non-negative integers and the harmonic oscillator spectra correspond to the recursive computation - with the creation and annihilation operators, respectively, playing the same role as the successor and predecessor in computability theory. Accordingly, this approach relates the classical computational model and the quantum physical model more directly than the Turing machine approach used earlier. Also, the application of Lambda calculus formalism and the associated denotational semantics (that is widely used in the classical computational paradigm involving recursive functions) for applications to computational paradigm based on quantum field theory is described. Finally, we explain where QFT and conventional paradigm depart from each other, and examine the concept of fixed points, phase transitions, programmability, emergent computation and related open problems.

Krishnamurthy, E. V.; Krishnamurthy, Vikram

215

NASA Astrophysics Data System (ADS)

Intravascular ultrasound (IVUS) is known to be the reference tool for preoperative vessel lesion assessments and for endovascular therapy planning. Nevertheless, IVUS echograms only provide subjective information about vessel wall lesions. Since changes in the vascular tissue stiffness are characteristic of vessel pathologies, catheter-based endovascular ultrasound elastography (EVE) has been proposed in the literature as a method for outlining the elastic properties of vessel walls. In this paper, the Lagrangian Speckle Model Estimator (LSME) is formulated for investigations in EVE, i.e., using a polar coordinate system. The method was implemented through an adapted version of the Levenberg-Marquardt minimization algorithm, using the optical flow equations to compute the Jacobbian matrix. The theoretical framework was validated with simulated ultrasound rf data of mechanically complex vessel wall pathologies. The results, corroborated with Ansys finite element software, demonstrated the potential of EVE to provide useful information about the heterogeneous nature of atherosclerotic plaques.

Maurice, Roch L.; Ohayon, Jacques; Finet, Gérard; Cloutier, Guy

2004-08-01

216

Quantum field theory for orthofermions and orthobosons

NASA Astrophysics Data System (ADS)

Orthofermi statistics is characterized by an exclusion principle which is more ``exclusive'' than Pauli's exclusion principle: an orbital state shall not contain more than one particle, no matter what the spin direction is. The wavefunction is antisymmetric in spatial indices alone with arbitrary symmetry in the spin indices. Orthobose statistics is corresponding Bose analog: the wavefunction is symmetric in spatial indices, with arbitrary symmetry in spin indices. We construct the quantum field theory of particles obeying these new kinds of quantum statistics. Non-relativistic as well as relativistic quantum field theories with interactions are considered. .

Mishra, A. K.; Rajasekaran, G.

2000-11-01

217

Coherent states formulation of polymer field theory.

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first direct numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well-known auxiliary-field (AF) framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields, and the action of the field theory has a fully explicit, semi-local, and finite-order polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF-CL simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies. PMID:24437909

Man, Xingkun; Delaney, Kris T; Villet, Michael C; Orland, Henri; Fredrickson, Glenn H

2014-01-14

218

Quantum field theory and gravity in causal sets

NASA Astrophysics Data System (ADS)

Causal set is a model of space time that allows to reconcile discreteness and manifest relativistic invariance. This is done by viewing space time as finite, partially ordered set. The elements of the set are viewed as points of space time, or events; the partial ordering between them is viewed as causal relations. It has been shown that, in discrete scenario, the information about causal relations between events can, indeed, approximate the metric. The goal of this thesis is to introduce matter fields and their Lagrangians into causal set context. This is a two step process. The first step is to re-define gauge fields, gravity, and distances in such a way that no reference to Lorentz index is made. This is done by defining gauge fields as two-point real valued functions, and gravitational field as causal structure itself. Once the above is done, Lagrangians have to be defined in a way that they don't refer to Lorentzian indices either. This is done by introducing a notion of type 1 and type 2 Lagrangian generators, coupled with respective machinery that "translates" each generator into corresponding Lagrangian. The fields that are subject to these generators are, respectively, defined as type 1 and type 2. The main difference between two kinds of fields is the prediction of different behavior in different dimensions of type 2 fields. However, despite our inability to travel to different dimensions, gravity was shown to be type 2 based on the erroneous predictions of its 4-dimensional behavior if it was viewed as type 1. However, no erroneous predictions are made if non-gravitational fields are viewed as either type 1 or type 2, thus the nature of the latter is still an open question. Finally, an attempt was made to provide interpretation of quantum mechanics that would allow to limit fluctuations of causal structure to allow some topological background. However, due to its controversial nature, it is placed in the Appendix.

Sverdlov, Roman M.

219

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

220

Bipartite field theories from D-branes

NASA Astrophysics Data System (ADS)

We develop tools for determining the gauge theory resulting from a configuration of Type IIB D3-branes probing a non-compact, toric Calabi-Yau 3-fold, in the presence of additional flavor D7-branes with general embeddings. Two main ingredients of our approach are dimer models and mirror symmetry. D7-branes with general embeddings are obtained by recombination of elementary D7-brane constituents. These tools are then used to engineer a large set of Bipartite Field Theories, a class of 4d, = 1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. Several explicit examples, including infinite families of models, associated to both planar and non-planar graphs are presented.

Franco, Sebastián; Uranga, Angel

2014-04-01

221

Shape Dynamics and Effective Field Theory

NASA Astrophysics Data System (ADS)

Shape dynamics is a gauge theory based on spatial diffeomorphism- and Weyl-invariance which is locally indistinguishable from classical general relativity. If taken seriously, it suggests that the space-time geometry picture that underlies general relativity can be replaced by a picture based on spatial conformal geometry. This classically well-understood trading of gauge symmetries opens new conceptual avenues in many approaches to quantum gravity. This paper focusses on the general implications for quantum gravity and effective field theory and considers the application of the shape dynamics picture in the exact renormalization group approaches to gravity, loop- and polymer-quantization approaches to gravity and low energy effective field theories. Also, the interpretation of known results is discussed through the shape dynamics picture, particularly holographic renormalization and the problem of time in canonical quantum gravity.

Koslowski, Tim A.

2013-05-01

222

Double field theory: a pedagogical review

NASA Astrophysics Data System (ADS)

Double field theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical presentation of DFT and its applications. We first introduce some basic ideas on T-duality and supergravity in order to proceed to the construction of generalized diffeomorphisms and an invariant action on the double space. Steps towards the construction of a geometry on the double space are discussed. We then address generalized Scherk-Schwarz compactifications of DFT and their connection to gauged supergravity and flux compactifications. We also discuss U-duality extensions and present a brief parcours on worldsheet approaches to DFT. Finally, we provide a summary of other developments and applications that are not discussed in detail in the review.

Aldazabal, Gerardo; Marqués, Diego; Núñez, Carmen

2013-08-01

223

Entropy Density for Relativistic Quantum Field Theory

NASA Astrophysics Data System (ADS)

We show how the nuclearity condition of Buchholz and Wichmann allows to define in the ground state a local entropy with the desired properties despite the fact that local algebras are type III. Generalization to temperature states is also possible so that thermodynamic functions also exist in the context of relativistic quantum field theory.

Narnhofer, Heide

224

A Modern Introduction to Quantum Field Theory

This book gives a clear exposition of quantum field theory at the graduate level and the contents could be covered in a two semester course or, with some effort, in a one semester course. The book is well organized, and subtle issues are clearly explained. The margin notes are very useful, and the problems given at the end of each

R Parthasarathy

2005-01-01

225

Magnetic Charge and Quantum Field Theory.

National Technical Information Service (NTIS)

A quantum field theory of magnetic and electric charge is constructed. It is verified to be relativistically invariant in consequence of the charge quantization condition eg/hc=n, an integer. This is more restrictive than Dirac's condition, which would al...

J. Schwinger

1965-01-01

226

General relativity invariance and string field theory

NASA Astrophysics Data System (ADS)

The general covariance principle in the string field theory is considered. The algebraic properties of the string Lie derivative are discussed. The string vielbein and spin connection are introduced and an action invariant under general co-ordinate transformation is proposed.

Arefeva, I. Ya.; Volovich, I. V.

1987-04-01

227

Cross Sections From Scalar Field Theory

NASA Technical Reports Server (NTRS)

A one pion exchange scalar model is used to calculate differential and total cross sections for pion production through nucleon- nucleon collisions. The collisions involve intermediate delta particle production and decay to nucleons and a pion. The model provides the basic theoretical framework for scalar field theory and can be applied to particle production processes where the effects of spin can be neglected.

Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel

2008-01-01

228

Finite quantum field theory in noncommutative geometry

We describe a self-interacting scalar field on a truncated sphere and perform the quantization using the functional (path) integral approach. The theory possesses full symmetry with respect to the isometries of the sphere. We explicitly show that the model is finite and that UV regularization automatically takes place.

H. Grosse; C. Klimcík; P. Presnajder

1996-01-01

229

Class Field Theory for Arithmetic Surfaces

In this paper we improve the results of K. Kato and S. Saito about the ramified class field theory of arithmetic surfaces and give an affirmative answer to the problem 2 of S. Bloch in Ann. of Math. 114(1981), pp.229-265

Qingchun Titan

1998-01-01

230

An Introduction to Effective Field Theory

NASA Astrophysics Data System (ADS)

This review summarizes effective field theory techniques, which are the modern theoretical tools for exploiting the existence of hierarchies of scale in a physical problem. The general theoretical framework is described and evaluated explicitly for a simple model. Power-counting results are illustrated for a few cases of practical interest, and several applications to quantum electrodynamics are described.

Burgess, C. P.

2007-11-01

231

The Vacuum Trajectory in Conventional Field Theory.

National Technical Information Service (NTIS)

The generation of a Pomeranchuk-like (or P) trajectory in the conventional field theory is discussed. This differs from the previously discussed fermion trajectory problem in several ways. The P trajectory in no way corresponds to an elementary particle o...

M. Gell-Mann M. L. Goldberger F. E. Low

1964-01-01

232

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

233

Monte Carlo approaches to effective field theories

NASA Astrophysics Data System (ADS)

In this paper, we explore the application of continuum Monte Carlo methods to effective field theory models. Effective field theories, in this context, are those in which a Fock space decomposition of the state is useful. These problems arise both in nuclear and condensed matter physics. In nuclear physics, much work has been done on effective field theories of mesons and baryons. While the theories are not fundamental, they should be able to describe nuclear properties at low energy and momentum scales. After describing the methods, we solve two simple scalar field theory problems; the polaron and two nucleons interacting through scalar meson exchange. The methods presented here are rather straightforward extensions of methods used to solve quantum mechanics problems. Monte Carlo methods are used to avoid the truncation inherent in a Tamm-Dancoff approach and its associated difficulties. Nevertheless, the methods will be most valuable when the Fock space decomposition of the states is useful. Hence, while they are not intended for ab initio studies of QCD, they may prove valuable in studies of light nuclei, or for systems of interacting electrons and phonons. In these problems, a Fock space decomposition can be used to reduce the number of degrees of freedom and to retain the rotational symmetries exactly. The problems we address here are comparatively simple, but offer useful initial tests of the method. We present results for the polaron and two non-relativistic nucleons interacting through scalar meson exchange. In each case, it is possible to integrate out the boson degrees of freedom exactly, and obtain a retarded form of the action that depends only upon the fermion paths. Here we keep the explicit bosons, though, since we would like to retain information about the boson components of the states and it will be necessary to keep these components in order to treat non-scalar of interacting bosonic fields.

Carlson, J.; Schmidt, K. E.

234

On perturbative field theory and twistor string theory

NASA Astrophysics Data System (ADS)

It is well-known that perturbative calculations in field theory can lead to far simpler answers than the Feynman diagram approach might suggest. In some cases scattering amplitudes can be constructed for processes with any desired number of external legs yielding compact expressions which are inaccessible from the point of view of conventional perturbation theory. In this thesis we discuss some attempts to address the nature of this underlying simplicity and then use the results to calculate some previously unknown amplitudes of interest. Witten's twistor string theory is introduced and the CSW rules at tree-level and one-loop are described. We use these techniques to calculate the one-loop gluonic MHV amplitudes in N=1 super-Yang-Mills as a verification of their validity and then proceed to evaluate the general MHV amplitudes in pure Yang-Mills with a scalar running in the loop. This latter amplitude is a new result in QCD. In addition to this, we review some recent on-shell recursion relations for tree-level amplitudes in gauge theory and apply them to gravity. As a result we present a new compact form for the n-graviton MHV amplitudes in general relativity. The techniques and results discussed are relevant to the understanding of the structure of field theory and gravity and the non-supersymmetric Yang-Mills amplitudes in-particular are pertinent to background processes at the LHC. The gravitational recursion relations provide new techniques for perturbative gravity and have some bearing on the ultraviolet properties of Einstein gravity.

Bedford, James

2007-09-01

235

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

236

Root Structures of Infinite Gauge Groups and Supersymmetric Field Theories

NASA Astrophysics Data System (ADS)

We show the relationship between critical dimensions of supersymmetric fundamental theories and dimensions of certain Jordan algebras. In our approach position vectors in spacetime or in superspace are endowed with algebraic properties that are present only in those critical dimensions. A uniform construction of super Poincaré groups in these dimensions will be shown. Some applications of these algebraic methods to hidden symmetries present in the covariant and interacting string Lagrangians and to superparticle will be discussed. Algebraic methods we develop will be shown to generate the root structure of some infinite groups that play the role of gauge groups in a second quantized theory of strings.

Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent

2013-11-01

237

A computational theory of visual receptive fields.

A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space-time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative agreement are obtained for (i) spatial on-center/off-surround and off-center/on-surround receptive fields in the fovea and the LGN, (ii) simple cells with spatial directional preference in V1, (iii) spatio-chromatic double-opponent neurons in V1, (iv) space-time separable spatio-temporal receptive fields in the LGN and V1, and (v) non-separable space-time tilted receptive fields in V1, all within the same unified theory. In addition, the paper presents a more general framework for relating and interpreting these receptive fields conceptually and possibly predicting new receptive field profiles as well as for pre-wiring covariance under scaling, affine, and Galilean transformations into the representations of visual stimuli. This paper describes the basic structure of the necessity results concerning receptive field profiles regarding the mathematical foundation of the theory and outlines how the proposed theory could be used in further studies and modelling of biological vision. It is also shown how receptive field responses can be interpreted physically, as the superposition of relative variations of surface structure and illumination variations, given a logarithmic brightness scale, and how receptive field measurements will be invariant under multiplicative illumination variations and exposure control mechanisms. PMID:24197240

Lindeberg, Tony

2013-12-01

238

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

239

Hydrodynamic flow structures in quantum field theory

The transport of matter is examined in the context of relativistic quantum transport theory for the case of neutral scalar fields. The goal is to formulate a theory valid off mass shell and out of equilibrium. We construct a conserved moment tensor which coincides with the ensemble average of the Noether tensor, or the improved energy-momentum tensor within an additive constant of the improvement term. Conditions for closure of the conservation equation are given for the phi/sup 4/ coupling. 8 references.

Carruthers, P.; Zachariasen, F.

1984-05-01

240

Hydrodynamic flow structures in quantum field theory

The transport of matter is examined in the context of relativistic quantum transport theory for the case of neutral scalar fields. The goal is to formulate a theory valid off mass shell and out of equilibrium. We construct a conserved moment tensor which coincides with the ensemble average of the Noether tensor, or the improved energy-momentum tensor with the ensemble average of the Noether tensor, or the improved energy-momentum tensor within an additive constant of the ''improvement'' term. Conditions for closure of the conservation equation are given for the phi/sup 4/ coupling.

Carruthers, P.; Zachariasen, F.

1984-11-15

241

Melonic Phase Transition in Group Field Theory

NASA Astrophysics Data System (ADS)

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher-dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of 4-dimensional models of quantum gravity.

Baratin, Aristide; Carrozza, Sylvain; Oriti, Daniele; Ryan, James; Smerlak, Matteo

2014-05-01

242

Gauge symmetry in background charge conformal field theory

We present a mechanism to construct four-dimensional charged massless Ramond states using the discrete states of a fivebrane Liouville internal conformal field theory. This conformal field theory has background charge, and admits an inner product which allows positive norm states. A connection among supergravity soliton solutions, Liouville conformal field theory, non-critical string theory and their gauge symmetry properties is given.

L. Dolan

1997-01-01

243

New theory of radiative energy transfer in free electromagnetic fields

A theory of radiative transfer in free, statistically stationary electromagnetic fields is presented which provides a model for energy transport that is rigorous within the framework of the stochastic theory of the classical field as well as within the framework of the theory of the quantized field. The present theory emphasizes the need for characterizing energy transport by means of

E. Wolf

1976-01-01

244

Twistor Diagrams and Quantum Field Theory.

NASA Astrophysics Data System (ADS)

Available from UMI in association with The British Library. Requires signed TDF. This thesis uses twistor diagram theory, as developed by Penrose (1975) and Hodges (1990c), to try to approach some of the difficulties inherent in the standard quantum field theoretic description of particle interactions. The resolution of these issues is the eventual goal of the twistor diagram program. First twistor diagram theory is introduced from a physical view-point, with the aim of studying larger diagrams than have been typically explored. Methods are evolved to tackle the double box and triple box diagrams. These lead to three methods of constructing an amplitude for the double box, and two ways for the triple box. Next this theory is applied to translate the channels of a Yukawa Feynman diagram, which has more than four external states, into various twistor diagrams. This provides a test of the skeleton hypothesis (of Hodges, 1990c) in these cases, and also shows that conformal breaking must enter into twistor diagrams before the translation of loop level Feynman diagrams. The issue of divergent Feynman diagrams is then considered. By using a twistor equivalent of the sum-over -states idea of quantum field theory, twistor translations of loop diagrams are conjectured. The various massless propagator corrections and vacuum diagrams calculated give results consistent with Feynman theory. Two diagrams are also found that give agreement with the finite parts of the Feynman "fish" diagrams of phi^4 -theory. However it is found that a more rigorous translation for the time-like fish requires new boundaries to be added to the twistor sum-over-states. The twistor diagram obtained is found to give the finite part of the relevant Feynman diagram.

O'Donald, Lewis

245

mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}

Galvao, C.A. [Universidade de Brasilia, Departamento de Fisica, 70.910 Brasilia DF, (Brasil)] [Universidade de Brasilia, Departamento de Fisica, 70.910 Brasilia DF, (Brasil); Nutku, Y. [TUeBITAK---Marmara Research Center, Research Institute for Basic Sciences, Department of Physics, 41470 Gebze (Turkey)] [TUeBITAK---Marmara Research Center, Research Institute for Basic Sciences, Department of Physics, 41470 Gebze (Turkey)

1996-12-01

246

Nonequilibrium perturbation theory for complex scalar fields

NASA Astrophysics Data System (ADS)

Real-time perturbation theory is formulated for complex scalar fields away from thermal equilibrium in such a way that dissipative effects arising from the absorptive parts of loop diagrams are approximately resummed into the unperturbed propagators. Low order calculations of physical quantities then involve quasiparticle occupation numbers which evolve with the changing state of the field system, in contrast with standard perturbation theory, where these occupation numbers are frozen at their initial values. The evolution equation of the occupation numbers can be cast approximately in the form of a Boltzmann equation. Particular attention is given to the effects of a nonzero chemical potential, and it is found that the thermal masses and decay widths of quasiparticle modes are different for particles and antiparticles.

Lawrie, I. D.; McKernan, D. B.

1997-02-01

247

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

248

Quantum sl n Toda field theories

NASA Astrophysics Data System (ADS)

We quantize sl n Toda field theories in a periodic lattice. We find the quantum exchange algebra in the diagonal monodromy (Bloch-wave) basis in the case of the defining representation. In the sl 3 case we extend the analysis also to the second fundamental representation. We clarify, in particular, the relation of Jimbo and Rosso's quantum R-matrix with the quantum R-matrix in the Bloch-wave basis.

Bonora, L.; Bonservizi, V.

1993-01-01

249

Refringence, field theory and normal modes

In a previous paper [Barceló C et al 2001 Class. Quantum Grav. 18 3595-610 (Preprint gr-qc\\/0104001)] 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 nontrivial background configuration. This observation explains the ubiquitous nature of the 'analogue models' for general relativity that have recently

Carlos Barceló; Stefano Liberati; Matt Visser

2002-01-01

250

A DFT Based Ligand Field Theory

A general and user-oriented ligand field (LF) theory – LFDFT with parameters adjusted to DFT energies of separate Slater Determinants (SD) of the partly filled dn shell [n=2(8), 3(7), 4(6) and 5] of transition metals (TM) complexes – is developed and tested using 22 well documented examples from the literature. These include CrIII, d3 and CoII d7 in octahedral and

M. Atanasov; C. Daul; C. Rauzy

251

Tachyon condensation in cubic superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the non-BPS D-brane or brane–anti-D-brane pair, the negative energy density cancels the brane tension. We study this conjecture using a cubic superstring field theory with insertion of a double-step inverse picture changing operator. We compute the tachyon potential at levels (1\\/2,1) and (2,6). In the first

I. Ya. Aref'eva; A. S. Koshelev; D. M. Belov; P. B. Medvedev

2002-01-01

252

Constraining noncommutative field theories with holography

An important window to quantum gravity phenomena in low energy noncom-mutative (NC) quantum field theories (QFTs) gets represented\\u000a by a specific form of UV\\/IR mixing. Yet another important window to quantum gravity, a holography, manifests itself in effective\\u000a QFTs as a distinct UV\\/IR connection. In matching these two principles, a useful relationship connecting the UV cutoff ?UV, the IR cutoff

Raul Horvat; Josip Trampetic

2011-01-01

253

Relativistic theory of gravity and a Brans-Dicke scalar field

NASA Astrophysics Data System (ADS)

The natural generalization of the relativistic theory of gravity (RTG) by incorporating a Brans-Dicke scalar field is discussed. The equation for a scalar-tensor gravitational field in Minkowski space and the expression for the total energy-momentum metric tensor of a gravitational field and nongravitational matter is derived from the variational principle with a gravitational Lagrangian quadratic in the first derivatives of the scalar and tensor gravitational potentials. The two-parameter spherically symmetrical static solution for vacuum equations with a zero mass tensor graviton was obtained. This solution has a true singular Schwarzschild surface. In the case of a nonzero mass graviton, an approximate nonsingular solution for the beginning of the universe was obtained. It is noted that in the frame of the scalar-tensor generalization of RTG, a nonsingular homogeneous isotropic cosmology can be represented, not only by cyclic models, but also by models with an infinitely expanding universe and a simultaneously decreasing gravitational scalar.

Tuniak, V. N.

1996-02-01

254

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

255

The flux-rope-fibre theory of solar magnetic fields

The flux-rope theory of solar magnetic fields is reviewed briefly and, together with the dynamo theory, compared with various observational results. Dynamo and related theories are based on fields controlled by the plasma, and it is shown that such fields cannot account for the strong surface fields or even emerge without becoming tangled. Observations which appear uniquely explicable in terms

J. H. Piddington

1978-01-01

256

Yangian superalgebras in conformal field theory

NASA Astrophysics Data System (ADS)

Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We then show that this symmetry is preserved by certain perturbations of the conformal field theory. The main examples are sigma models of the supergroups PSL(N|N), OSP(2N+2|2N) and D(2,1;?) away from the WZW point. Further there are the OSP(2N+2|2N) Gross-Neveu models and current-current perturbations of ghost systems, both for the disc as world-sheet. The latter we show to be equivalent to CP sigma models, while the former are conjecturally dual to supersphere sigma models.

Creutzig, Thomas

2011-08-01

257

Lagrangian transport experiments in the MLT region

In order to evaluate material transports in the upper mesosphere and lower thermosphere (MLT) region, Lagrangian transport experiments are performed using wind fields simulated by the Kyushu University middle atmosphere general circulation model (Miyahara and Miyoshi, 1997; Miyahara et al, 1993). The Lagrangian mean meridional circulation is different from the residual mean circulation defined by the Transformed Eulerian Mean equation

S. Watanabe; S. Miyahara; Y. Miyoshi

1999-01-01

258

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

259

General Field Theory for Vortex Structure and Interaction.

National Technical Information Service (NTIS)

The purpose of this work is to present a general field theory describing the structure and interaction of vortices, both atmospheric and extraterrestrial. This field theory is characterized by four main elements: (1) New laws of physics, (2) New mathemati...

F. H. Nicholson

1983-01-01

260

New mathematical structures in renormalizable quantum field theories

NASA Astrophysics Data System (ADS)

Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the role they can play in future developments.

Kreimer, Dirk

2003-01-01

261

Some aspects of field equations in generalized theories of gravity

NASA Astrophysics Data System (ADS)

A class of theories of gravity based on a Lagrangian L=L(Rabcd,gab) which depends on the curvature and metric—but not on the derivatives of the curvature tensor—is of interest in several contexts including in the development of the paradigm that treats gravity as an emergent phenomenon. This class of models contains, as an important subset, all Lanczos-Lovelock models of gravity. I derive several identities and properties which are useful in the study of these models and clarify some of the issues that seem to have received insufficient attention in the past literature.

Padmanabhan, T.

2011-12-01

262

On the Construction of Quantum Field Theories with Factorizing S-Matrices

NASA Astrophysics Data System (ADS)

The subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two-dimensional Minkowski space. The input in this construction is not a classical Lagrangian, but rather a prescribed factorizing S-matrix, i.e. the inverse scattering problem for such quantum field theories is studied. For a large class of factorizing S-matrices, certain associated quantum fields, which are localized in wedge-shaped regions of Minkowski space, are constructed explicitely. With the help of these fields, the local observable content of the corresponding model is defined and analyzed by employing methods from the algebraic framework of quantum field theory. The abstract problem in this analysis amounts to the question under which conditions an algebra of wedge-localized observables can be used to generate a net of local observable algebras with the right physical properties. The answer given here uses the so-called modular nuclearity condition, which is shown to imply the existence of local observables and the Reeh-Schlieder property. In the analysis of the concrete models, this condition is proven for a large family of S-matrices, including the scattering operators of the Sinh-Gordon model and the scaling Ising model as special examples. The so constructed models are then investigated with respect to their scattering properties. They are shown to solve the inverse scattering problem for the considered S-matrices, and a proof of asymptotic completeness is given.

Lechner, Gandalf

2006-11-01

263

XXIVth International Symposium on Lattice Field Theory

NASA Astrophysics Data System (ADS)

Lattice 2006, the XXIV International Symposium on Lattice Field Theory, was held from July 23-28, 2006 at the Starr Pass Hotel near Tucson, Arizona, USA, hosted by the University of Arizona Physics Department. The scientific program contained 25 plenary session talks and 193 parallel session contributions (talks and posters). Topics in lattice QCD included: hadron spectroscopy; hadronic interactions and structure; algorithms, machines, and networks; chiral symmetry; QCD confinement and topology; quark masses, gauge couplings, and renormalization; electroweak decays and mixing; high temperature and density; and theoretical developments. Topics beyond QCD included large Nc, Higgs, SUSY, gravity, and strings.

2006-12-01

264

Drift estimation from a simple field theory

Given the outcome of a Wiener process, what can be said about the drift and diffusion coefficients? If the process is stationary, these coefficients are related to the mean and variance of the position displacements distribution. However, if either drift or diffusion are time-dependent, very little can be said unless some assumption about that dependency is made. In Bayesian statistics, this should be translated into some specific prior probability. We use Bayes rule to estimate these coefficients from a single trajectory. This defines a simple, and analytically tractable, field theory.

Mendes, F. M.; Figueiredo, A. [Instituto de Fisica, Universidade de Brasilia, CP: 04455, 70919-970-Brasilia (Brazil)

2008-11-06

265

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

266

Exact integrability in quantum field theory

The treatment of exactly integrable systems in various branches of two-dimensional classical and quantum physics has recently been placed in a unified framework by the development of the quantum inverse method. This method consolidates a broad range of developments in classical nonlinear wave (soliton) physics, statistical mechanics, and quantum field theory. The essential technique for analyzing exactly integrable quantum systems was invested by Bethe in 1931. The quantum-mechanical extension of the inverse scattering method and its relationship to the methods associated with Bethe's ansatz are examined here. (RWR)

Thacker, H.B.

1980-08-01

267

Tame class field theory for arithmetic schemes

We extend the unramified class field theory for arithmetic schemes of K. Kato\\u000aand S. Saito to the tame case. Let $X$ be a regular proper arithmetic scheme\\u000aand let $D$ be a divisor on $X$ whose vertical irreducible components are\\u000anormal schemes.\\u000a Theorem: There exists a natural reciprocity isomorphism \\\\[ \\\\rec_{X,D}:\\u000a\\\\CH_0(X,D) \\\\liso \\\\tilde \\\\pi_1^t(X,D)^\\\\ab\\\\. \\\\] Both groups are

Alexander Schmidt

2005-01-01

268

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

269

Conformal field theory and hyperbolic geometry

NASA Astrophysics Data System (ADS)

We examine the correspondence betweeen the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. Considering domain boundaries in critical systems and the invariance of the hyperbolic length allows a new interpretation of the basic equation of conformal covariance. The scale factors gain a physical interpretation. We exhibit a fully factored form for the three-point function. An infinite series of minimal models with limit point c=-2 is discovered. A correspondence between the anomalous dimension and the angle of certain hyperbolic figures emerges.

Kleban, P.; Vassileva, I.

1994-06-01

270

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

271

The combined Lagrangian advection method

NASA Astrophysics Data System (ADS)

We present and test a new hybrid numerical method for simulating layerwise-two-dimensional geophysical flows. The method radically extends the original Contour-Advective Semi-Lagrangian (CASL) algorithm [5] by combining three computational elements for the advection of general tracers (e.g. potential vorticity, water vapor, etc.): (1) a pseudo-spectral method for large scales, (2) Lagrangian contours for intermediate to small scales, and (3) Lagrangian particles for the representation of general forcing and dissipation. The pseudo-spectral method is both efficient and highly accurate at large scales, while contour advection is efficient and accurate at small scales, allowing one to simulate extremely fine-scale structure well below the basic grid scale used to represent the velocity field. The particles allow one to efficiently incorporate general forcing and dissipation.

Dritschel, David G.; Fontane, Jérôme

2010-08-01

272

Bondi Mass in Classical Field Theory

NASA Astrophysics Data System (ADS)

We discuss three classical field theories based on the wave equation: scalar field, electrodynamics and linearized gravity. Certain generating formula on a hyperboloid and on a null surface are derived for them. The linearized Einstein equations are analyzed around the null infinity. It is shown how the dynamics can be reduced to gauge invariant quanitities in a quasi-local way. The quasi-local gauge-invariant ``density'' of the Hamiltonian is derived on the hyperboloid and on the future null infinity cal J+. The result gives a new interpretation of the Bondi mass loss formula. We show also how to define the angular momentum. Starting from an affine approach for Einstein equations we obtain variational formulae for Bondi--Sachs type metrics related to energy and angular momentum generators. The original van der Burg asymptotic hierarchy is revisited and the relations between linearized and asymptotic nonlinear situations are established. We discuss also supertranslations, Newman--Penrose charges and Janis solutions.

Jezierski, J.

1998-03-01

273

Causality Is Inconsistent With Quantum Field Theory

Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non-vanishing probabilities for both negative energy particles in the forward-through-time direction and positive energy antiparticles in the backwards-through-time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.

Wolf, Fred Alan [Global Quantum Physics Educational Company, San Francisco CA (United States)

2011-11-29

274

Renormalized thermal entropy in field theory

Standard entropy calculations in quantum field theory, when applied to a subsystem of definite volume, exhibit area-dependent UV divergences that make a thermodynamic interpretation troublesome. In this paper we define a renormalized entropy which is related with the Newton-Wigner position operator. Accordingly, whenever we trace over a region of space, we trace away degrees of freedom that are localized according to Newton-Wigner localization but not in the usual sense. We consider a free scalar field in d+1 spacetime dimensions prepared in a thermal state and we show that our entropy is free of divergences and has a perfectly sound thermodynamic behavior. In the high temperature/big volume limit our results agree with the standard QFT calculations once the divergent contributions are subtracted from the latter. In the limit of low temperature/small volume the entropy goes to zero but with a different dependence on the temperature.

Cacciatori, Sergio L.; Costa, Fabio; Piazza, Federico [Dipartimento di Scienze Fisiche e Matematiche, Universita dell'Insubria, Via Valleggio 11, I-22100 Como (Italy); Institut fuer Quantenoptik und Quanteninformation (IQOQI), Oesterreichische Akademie der Wissenschaften, Boltzmanngasse 3, A-1090 Wien (Austria); Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5 (Canada)

2009-01-15

275

PT-Symmetric Quantum Field Theory

In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H{sup {dagger}}) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.

Bender, Carl M. [Physics Department, Washington University, St. Louis, MO 63130 (United States)

2011-09-22

276

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

277

After some necessary recalls on the nonlinear theory of thermoelectroelasticity in piezoelectric crystals, asserting the need of constitutive equations which derive from a rotationally invariant energy function, this paper presents the governing equations for a small vibration superimposed on a bias originated by a slow and homogeneous temperature variation from a well-defined reference state. Thereafter, the authors define the effective coefficients appearing in the linearized incremental dynamic balance equations for linear momentum and electrical charge in Lagrange configuration, not omitting associated boundary conditions. The main features of these coefficients are discussed and explicit relations with more conventionally defined coefficients are given. Determination of numerical values of the proposed effective coefficients and examples of their use in the higher order modeling of static frequency-temperature characteristics of either bulk acoustic wave or surface acoustic wave devices are given in a companion paper. PMID:11681360

Dulmet, B; Bourquin, R

2001-10-01

278

Homogeneous cosmologies as group field theory condensates

NASA Astrophysics Data System (ADS)

We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the `condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.

Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo

2014-06-01

279

Refringence, field theory and normal modes

NASA Astrophysics Data System (ADS)

In a previous paper [Barceló C et al 2001 Class. Quantum Grav. 18 3595-610 (Preprint gr-qc/0104001)] 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 nontrivial background configuration. This observation explains the ubiquitous nature of the 'analogue models' for general relativity that have recently been developed based on condensed matter physics. In the simple (single scalar field) situation analysed 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 Eötvös 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 'analogue gravity' is rather generic.

Barceló, Carlos; Liberati, Stefano; Visser, Matt

2002-06-01

280

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

281

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

282

Wigner trajectory characteristics in phase space and field theory

NASA Astrophysics Data System (ADS)

Exact characteristic trajectories are specified for the time-propagating Wigner phase-space distribution function. They are especially simple - indeed, classical - for the quantized simple harmonic oscillator, which 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. Applications to duality transformations in field theory are discussed.

Curtright, Thomas; Zachos, Cosmas

1999-02-01

283

Equal rank embedding and its related construction to superconformal field theories

NASA Astrophysics Data System (ADS)

We studied the GKRS construction of an Euler multiplet of semisimple complex Lie algebras and extended the construction to basic Lie superalgebras. We observed that the Kostant's cubic Dirac operators of these two algebras are in a similar form and, in the case of Lie algebras, are analogous to supercurrents in superconformal field theories. At the level of representation theory, we studied the analogy between the GKRS construction of the Euler multiplet of semisimple complex Lie algebras and the Kazama-Suzuki construction of super-Kac-Moody algebras associated with superconformal field theories. The Euler multiplets constructed by the GKRS method were found to be the intrinsic ground states of superconformal theories. The minimum eigenvalues of the Kostant operator in the GKRS construction and of energy-momentum tensor in the Kazama-Suzuki construction were derived from the Euler multiplet and were shown to be zero. We also studied the gauged supersymmetric Wess-Zumino-Witten Lagrangian and derived the superconformal generators, supercurrents and energy-momentum tensors, in the SU(2)/U(1) case.

Pengpan, Teparksorn

284

Effective Lagrangian for Skyrmion physics

NASA Astrophysics Data System (ADS)

The effective chiral Lagrangian for low-energy pion-Skyrmion physics is considered as an expansion in powers of (??), where ? is the chiral field. The O((??)2) term is the nonlinear ?-model Lagrangian L2. Two theoretical approaches to the higher-order terms are examined. The first involves integration over fermion degrees of freedom. The O((??)4) terms obtained this way, together with L2, are found to be consistent with low-energy ?? phase shifts-in particular, in the dominant ? and ? channels. In the second approach, an effective pion Lagrangian is generated by integrating some simple chiral meson-field Lagrangians over the heavy mesons. At O((??)4) two terms are found: a term L4,? of Skyrme form, with a model-independent coefficient determined by the ? mass, and a non-Skyrme term L4,?, the coefficient of which is more model dependent and determined by the ? mass; both terms are compatible with the fermion integration results. It is concluded that the O((??)4) terms are well established theoretically, and in good qualitative agreement with pion data. These terms do not, however, stabilize the soliton. Some discussion of the possible stabilizing effects of O((??)6) terms is given.

Aitchison, Ian J. R.; Fraser, Caroline M.; Miron, Paul J.

1986-04-01

285

Modifications to the Lagrangian particle dispersion model.

National Technical Information Service (NTIS)

An advanced stochastic Lagrangian Particle Dispersion Model (LPDM) is used by the Atmospheric Technologies Group to simulate contaminant transport. The model uses time-dependent three-dimensional fields of wind and turbulence to determine the location of ...

R. L. Buckley B. L. O'Steen

1997-01-01

286

Reggeon field theory for large Pomeron loops

NASA Astrophysics Data System (ADS)

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 ? throughout the evolution at least one of the colliding objects is dilute. Importantly, at some values of ? 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 [2, 3] and [4-6]. 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 [4-6] 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.

Altinoluk, Tolga; Kovner, Alex; Levin, Eugene; Lublinsky, Michael

2014-04-01

287

Mean field theory of charged dendrimer molecules.

Using self-consistent field theory (SCFT), we study the conformational properties of polyelectrolyte dendrimers. We compare results for three different models of charge distributions on the polyelectrolytes: (1) a smeared, quenched charge distribution characteristic of strong polyelectrolytes; (2) a smeared, annealed charge distribution characteristic of weak polyelectrolytes; and (3) an implicit counterion model with Debye-Huckel interactions between the charged groups. Our results indicate that an explicit treatment of counterions is crucial for the accurate characterization of the conformations of polyelectrolyte dendrimers. In comparing the quenched and annealed models of charge distributions, annealed dendrimers were observed to modulate their charges in response to the density of polymer monomers, counterions, and salt ions. Such phenomena is not accommodated within the quenched model of dendrimers and is shown to lead to significant differences between the predictions of quenched and annealed model of dendrimers. In this regard, our results indicate that the average dissociated charge ? inside the dendrimer serves as a useful parameter to map the effects of different parametric conditions and models onto each other. We also present comparisons to the scaling results proposed to explain the behavior of polyelectrolyte dendrimers. Inspired by the trends indicated by our results, we develop a strong segregation theory model whose predictions are shown to be in very good agreement with the numerical SCFT calculations. PMID:22128954

Lewis, Thomas; Pryamitsyn, Victor; Ganesan, Venkat

2011-11-28

288

Holographic entanglement entropy of nonlocal field theories

NASA Astrophysics Data System (ADS)

We study the holographic entanglement entropy of nonlocal field theories at both extremality and finite temperature. The gravity duals, constructed by Nozaki et al. [J. High Energy Phys. 10 (2012) 193], are characterized by a parameter w. Both the zero-temperature backgrounds and the finite-temperature counterparts are exact solutions of Einstein-Maxwell-dilaton theory. For the extremal case we consider the examples where the entangling regions are a strip and a sphere. We find that the leading-order behavior of the entanglement entropy always exhibits a volume law when the size of the entangling region is sufficiently small. We also clarify the condition under which the next-to-leading-order result is universal. For the finite-temperature case we obtain analytic expressions in both the high-temperature and low-temperature limits. In the former case the leading-order result approaches the thermal entropy, while the finite contribution to the entanglement entropy at extremality can be extracted by taking the zero-temperature limit in the latter case. Moreover, we observe some peculiar properties of the holographic entanglement entropy when w=1.

Pang, Da-Wei

2014-06-01

289

Effective field theory calculations of NN ? NN?

NASA Astrophysics Data System (ADS)

In this review, we present the recent advances for calculations of the reactions NN ? NN? using chiral effective field theory ?EFT. Discussed are the next-to-next-to leading order (N2LO) loop contributions with nucleon and Delta-isobar for near threshold s-wave pion-production. Results of recent experimental pion-production data for energies close to the threshold are analyzed. Several particular applications are discussed: (i) it is shown how the measured charge symmetry (CS) violating pion-production reaction can be used to extract the strong interaction contribution to the proton-neutron mass difference; (ii) the role of NN ? NN? for the extraction of the pion-nucleon scattering lengths from pionic atoms data is illuminated.

Baru, Vadim; Hanhart, Christoph; Myhrer, Fred

2014-04-01

290

Integrable Conformal Field Theory - A Case Study

Over the last decades, 2-dimensional conformal field theory has been developed into a powerful tool that has been applied to problems in diverse branches of physics and mathematics. Models are usually solved algebraically by exploiting certain infinite dimensional symmetries. But the presence of sufficient world-sheet symmetry is a rather exceptional feature, one that is e.g. not present for curved string backgrounds at generic points in moduli space. In this note I review some recent work which aims at computing spectra of conformal sigma models without spectrum generating symmetries. Our main results are illustrated at the example of complex projective superspace (C) P{sup N-1|N}. This note is based on several publications with C. Candu, T. Creutzig, V. Mitev, T. Quella and H. Saleur.

Schomerus, Volker [DESY Hamburg, Theory Group, Notkestrasse 85, D-22607 Hamburg (Germany)

2010-06-17

291

Takiff superalgebras and conformal field theory

NASA Astrophysics Data System (ADS)

A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an Abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalization of Sugawara’s construction is shown to give rise to a copy of the Virasoro algebra and so, presumably, to a conformal field theory. Evidence for this is detailed for the extension of the affinization of the superalgebra \\mathfrak {gl} ( 1 \\vert 1): its highest weight irreducible modules are classified using spectral flow, the irreducible supercharacters are computed and a continuum version of the Verlinde formula is verified to give non-negative integer structure coefficients. Interpreting these coefficients as those of the Grothendieck ring of fusion, partial results on the true fusion ring and its indecomposable structures are deduced.

Babichenko, Andrei; Ridout, David

2013-03-01

292

Applied Effective Field Theory to Nuclear Matter

NASA Astrophysics Data System (ADS)

An important issue when trying to apply effective field theory (EFT) methods to the nuclear matter problem is the identification of the expansion parameter. A perturbative matching calculation shows how the radius of convergence in free space is related to the radius of convergence in nuclear matter, and gives an estimate of the expansion parameter. Conventional approaches to nuclear matter find that the binding energy is sensitive to off-shell effects that depend on the two-body potential. (Coester et al., Phys. Rev. C 1), 769(1970)^, (M. I. Haftel and F. Tabakin, Phys. Rev. C 3), 921(1971) [4] In an EFT approach, observables should be independent of off-shell effects. The resolution of this discrepancy is discussed.

Tirfessa, Negussie; Furnstahl, R. J.

1999-10-01

293

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

294

Correlation functions in conformal Toda field theory I

Two-dimensional {sl}(n) quantum Toda field theory on a sphere is considered. This theory provides an important example of conformal field theory with higher spin symmetry. We derive the three-point correlation functions of the exponential fields if one of the three fields has a special form. In this case it is possible to write down and solve explicitly the differential equation

V. A. Fateev; A. V. Litvinov

2007-01-01

295

Parity-violating photon circular polarization in nd 3H with effective field theory at thermal energy

NASA Astrophysics Data System (ADS)

We study the parity-violating effects in nd 3H process using pionless effective field theory (EFT( /) at thermal energy. For the weak NN interaction the parity-violating Lagrangian contains five independent low-energy coupling constants (LECs). One can fix the coupling constants by comparison of the calculated observables with a sufficient number of experimental data. So, we need five observables to obtain LECs. One of the five parity-violating observables is the photon circular polarization ( in nd 3H process. We calculate at the leading order in terms of LECs. We compare our results with the previous calculation based on the model of Desplanques, Donoghue and Holstein.

Moeini Arani, M.; Bayegan, S.

2013-09-01

296

Topological field theory of dynamical systems.

Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the "edge of chaos." Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed. PMID:23020473

Ovchinnikov, Igor V

2012-09-01

297

Topological field theory of dynamical systems

NASA Astrophysics Data System (ADS)

Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (-symmetry). As many other supersymmetries, -symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken -symmetry, chaotic models with -symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with -symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the ``edge of chaos.'' Goldstone theorem stands behind spatio-temporal self-similarity of -broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of -broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. -symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.

Ovchinnikov, Igor V.

2012-09-01

298

Operator Approach to the Gluing Theorem in String Field Theory.

National Technical Information Service (NTIS)

An algebraic proof of the Gluing Theorem at tree level of perturbation theory in String Field Theory is given. Some applications of the theorem to closed string non-polynomial action are briefly discussed.

A. Abdurrahman J. Bordes C. Lara

1999-01-01

299

Higher-dimensional conformal field theories in the Coulomb branch

NASA Astrophysics Data System (ADS)

We use the AdS/CFT correspondence to study flows of N=4 SYM to non-conformal theories. The dual geometries can be seen as sourced by a Wigner's semicircle distribution of D3 branes. We consider two cases, the first case corresponds to a point in the Coulomb branch and the theory flows to a six-dimensional conformal field theory. In the second case a mass is introduced for a hypermultiplet and the theory flows to a five-dimensional conformal field theory. We argue from the gravity and the field theory side that the low energy theories correspond to the (2,0) theory in six dimensions and to a theory with exceptional global symmetry E in five dimensions.

Hoyos, Carlos

2011-01-01

300

Nonlinear gravitational-field equations in the special theory of relativity

NASA Astrophysics Data System (ADS)

A method is proposed for the consideration of field nonlinearity which is based on the fact that the structure of the Lagrangian expressed through the potential of the field and its derivatives is not prescribed beforehand but is derived as a result of the solution in phase space of the self-action equation whose unknown is the field Lagrangian. It is shown that this equation has a solution and that the Lagrangian is nonpolynomial with respect to the field potential. The gravitational-field equations which follow from the variational principle are found to be structurally similar to the general-relativity equations and coincide with them in the linear approximation. Equations of other fields with allowance for gravitation are constructed along with the equation of motion of a test particle in a gravitational field.

Razgovorov, N. N.

1983-08-01

301

Quantum gravity, field theory and signatures of noncommutative spacetime

A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with\\u000a emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what extent noncommutative\\u000a gauge theories may be regarded as gauge theories of gravity. UV\\/IR mixing is explained in detail and we describe

Richard J. Szabo

2010-01-01

302

The Physical Renormalization of Quantum Field Theories

The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi-scale analytic renormalization scheme based on gauge-invariant Green's functions, in which the scale ambiguity problem is reduced since physical kinematic invariants determine the arguments of the couplings.

Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC

2007-02-20

303

On the conformal field theory of the Higgs branch

We study 1+1-dimensional theories of vector and hypermultiplets with (4,4) supersymmetry. Despite strong infrared fluctuations, these theories flow in general to distinct conformal field theories on the Coulomb and Higgs branches. In some cases there may be a quantum Higgs theory even when there is no classical Higgs branch. The Higgs branches of certain such theories provide a framework for

Edward Witten

1997-01-01

304

Lorentz invariance in heavy particle effective theories

NASA Astrophysics Data System (ADS)

Employing induced representations of the Lorentz group (Wigner’s little group construction), formalism for constructing heavy particle effective Lagrangians is developed, and Lagrangian constraints enforcing Lorentz invariance of the S matrix are derived. The relationship between Lorentz invariance and reparametrization invariance is established and it is shown why a standard ansatz for implementing reparametrization invariance in heavy fermion effective Lagrangians breaks down at order 1/M4. Formalism for fields of arbitrary spin and for self-conjugate fields is presented, and the extension to effective theories of massless fields is discussed.

Heinonen, Johannes; Hill, Richard J.; Solon, Mikhail P.

2012-11-01

305

Complementary Analysis of the Field Perturbation Theory of Superconductivity

We reexamine the Nambu–Gorkov perturbation theory of superconductivity. We suggest that any field perturbation theory of superconductivity\\u000a should be based on the Bogoliubov–Valatin (BV) quasi-particles. We show that two such different fields (and two additional\\u000a analogous fields) may be constructed on the basis of this suggestion. The Nambu field is only one of them. For the field that\\u000a is different

Moshe Dayan

2006-01-01

306

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

307

Nonlinear equations of the gravitational field in the special theory of relativity

NASA Astrophysics Data System (ADS)

It is proposed that the nonlinearity of the field be taken into account with the help of a method which essentially consists of the fact that the structure of the Lagrangian, expressed in terms of the potential of the field and its derivatives, is not known a priori, but is obtained from a solution of the self-action equation in phase space in which the Lagrangian is the unknown. This equation has a solution and the Lagrangian turns out to be a nonpolynomial function with respect to the field potential. The gravitational field equations following from the variational principle have a similar structure to the equations of general relativity and coincide with them in the linear approximation. The equations of other fields taking into account gravitation, as well as the equation of motion of a test particle in a gravitational field, are constructed.

Razgovorov, N. N.

1983-08-01

308

Cluster Mass Inference via Random Field Theory

Cluster extent and voxel intensity are two widely used statistics in neuroimaging inference. Cluster extent is sensitive to spatially extended signals while voxel intensity is better for intense but focal signals. In order to leverage strength from both statistics, several nonparametric permutation methods have been proposed to combine the two methods. Simulation studies have shown that of the different cluster permutation methods, the cluster mass statistic is generally the best. However, to date, there is no parametric cluster mass inference method available. In this paper, we propose a cluster mass inference method based on random field theory (RFT). We develop this method for Gaussian images, evaluate it on Gaussian and Gaussianized t-statistic images and investigate its statistical properties via simulation studies and real data. Simulation results show that the method is valid under the null hypothesis and demonstrate that it can be more powerful than the cluster extent inference method. Further, analyses with a single-subject and a group fMRI dataset demonstrate better power than traditional cluster extent inference, and good accuracy relative to a gold-standard permutation test.

Zhang, Hui; Nichols, Thomas E.; Johnson, Timothy D.

2009-01-01

309

Logarithmic conformal field theory: a lattice approach

NASA Astrophysics Data System (ADS)

Logarithmic conformal field theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self-avoiding walks, etc), or of critical points in several classes of disordered systems (transition between plateaux in the integer and spin quantum Hall effects). Much progress in their understanding has been obtained by studying algebraic features of their lattice regularizations. For reasons which are not entirely understood, the non-semi-simple associative algebras underlying these lattice models—such as the Temperley-Lieb algebra or the blob algebra—indeed exhibit, in finite size, properties that are in full correspondence with those of their continuum limits. This applies not only to the structure of indecomposable modules, but also to fusion rules, and provides an ‘experimental’ way of measuring couplings, such as the ‘number b’ quantifying the logarithmic coupling of the stress-energy tensor with its partner. Most results obtained so far have concerned boundary LCFTs and the associated indecomposability in the chiral sector. While the bulk case is considerably more involved (mixing in general left and right moving sectors), progress has also recently been made in this direction, uncovering fascinating structures. This study provides a short general review of our work in this area.

Gainutdinov, A. M.; Jacobsen, J. L.; Read, N.; Saleur, H.; Vasseur, R.

2013-12-01

310

Neutrinoless double ? decay and effective field theory

NASA Astrophysics Data System (ADS)

We analyze neutrinoless double ? decay (0??? decay) mediated by heavy particles from the standpoint of effective field theory. We show how symmetries of the 0???-decay quark operators arising in a given particle physics model determine the form of the corresponding effective, hadronic operators. We classify the latter according to their symmetry transformation properties as well as the order at which they appear in a derivative expansion. We apply this framework to several particle physics models, including R-parity violating supersymmetry (RPV SUSY) and the left-right symmetric model (LRSM) with mixing and a right-handed Majorana neutrino. We show that, in general, the pion exchange contributions to 0??? decay dominate over the short-range four-nucleon operators. This confirms previously published RPV SUSY results and allows us to derive new constraints on the masses in the LRSM. In particular, we show how a nonzero mixing angle ? in the left-right symmetry model produces a new potentially dominant contribution to 0??? decay that substantially modifies previous limits on the masses of the right-handed neutrino and boson stemming from constraints from 0??? decay and vacuum stability requirements.

Prézeau, G.; Ramsey-Musolf, M.; Vogel, Petr

2003-08-01

311

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

312

D-Branes, Tachyons, and String Field Theory

In these notes we provide a pedagogical introduction to the subject of\\u000atachyon condensation in Witten's cubic bosonic open string field theory. We use\\u000aboth the low-energy Yang-Mills description and the language of string field\\u000atheory to explain the problem of tachyon condensation on unstable D-branes. We\\u000agive a self-contained introduction to open string field theory using both\\u000aconformal field

Washington Taylor; Barton Zwiebach

2003-01-01

313

Quantum Field Theory in the Limit x<<1

NASA Astrophysics Data System (ADS)

The asymptotic high momentum behavior of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x<<1. Particular emphasis is paid to theories with interactions involving more than one field where it is found that a matrix renormalization is necessary. Asymptotic scaling forms, in agreement with Regge theory, are derived for the elastic two-particle scattering amplitude and verified in one-loop renormalization group improved perturbation theory, corresponding to the summation of leading logs to all orders. We give explicit forms for the Regge trajectories of different scalar theories in this approximation and determine the signatures.

Stephens, C. R.; Weber, A.; López Vieyra, J. C.; Hess, P. O.

314

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

315

Bosons after Symmetry Breaking in Quantum Field Theory

We present a unified description of the spontaneous symmetry breaking and its associated bosons in fermion field theory. There is no Goldstone boson in the fermion field theory models of Nambu-Jona-Lasinio, Thirring and QCD$_2$ after the chiral symmetry is spontaneously broken in the new vacuum. The defect of the Goldstone theorem is clarified, and the \\

Takehisa Fujita; Makoto Hiramoto; Hidenori Takahashi

2007-01-01

316

D-branes as tachyon lumps in string field theory

It has been conjectured that the tachyonic lump solution of the open bosonic string field theory describing a D-brane represents a D-brane of one lower dimension. We place the lump on a circle of finite radius and develop a variant of the level expansion scheme that allows systematic account of all higher derivative terms in the string field theory action,

Nicolas Moeller; Barton Zwiebach; Ashoke Sen

2000-01-01

317

A Review on Tachyon Condensation in Open String Field Theories

We review the recent studies of tachyon condensation in string field theory. After introducing the open string field theory both for bosonic string and for superstring, we use them to examine the conjecture that the unstable configurations of the D-brane will decay into the `closed string vacuum' through the tachyon condensation. And we describe the attemps to construct a lower

Kazuki Ohmori

2001-01-01

318

Vacuum string field theory without matter-ghost factorization

We show that vacuum string field theory with the singular kinetic operator conjectured by Gaiotto, Rastelli, Sen and Zwiebach can be obtained by field redefinition from a regular theory constructed by Takahashi and Tanimoto. We solve the equation of motion both by level truncation and by a series expansion using the regulated butterfly state, and we find evidence that the

Nadav Drukker; Yuji Okawa

2005-01-01

319

NASA Astrophysics Data System (ADS)

The global U-dualities of extended supergravity have played a central role in differentiating the distinct classes of extremal black hole solutions. When the U-duality group satisfies certain algebraic conditions, as is the case for a broad class of supergravities, the extremal black holes enjoy a further symmetry known as Freudenthal duality (F-duality), which although distinct from U-duality preserves the Bekenstein-Hawking entropy. Here it is shown that, by adopting the doubled Lagrangian formalism, F-duality, defined on the doubled field strengths, is not only a symmetry of the black hole solutions, but also of the equations of motion themselves. A further role for F-duality is introduced in the context of world-sheet actions. The Nambu-Goto world-sheet action in any (t, s) signature spacetime can be written in terms of the F-dual. The corresponding field equations and Bianchi identities are then related by F-duality allowing for an F-dual formulation of Gaillard-Zumino duality on the world-sheet. An equivalent polynomial ‘Polyakov-type’ action is introduced using the so-called black hole potential. Such a construction allows for actions invariant under all groups of type E7, including E7 itself, although in this case the stringy interpretation is less clear.

Borsten, L.; Duff, M. J.; Ferrara, S.; Marrani, A.

2013-12-01

320

On quantization of field theories in polymomentum variables

Polymomentum canonical theories, which are manifestly covariant multiparameter generalizations of the Hamiltonian formulation to field theory, are considered as a possible basis of quantization. We arrive at a multi-parameter hypercomplex generalization of quantum mechanics to field theory in which complex numbers and a time parameter are replaced by the space-time Clifford algebra and space-time variables appearing on equal footing. The

Igor V. Kanatchikov; Igor V

1998-01-01

321

Conformal field theory, triality and the monster group

From an even self-dual N-dimensional lattice, Lambda, it is always possible to construct two (chiral) conformal field theories, an untwisted theory H (Lambda), and Z2-twisted theory H~(Lambda), constructed using the reflection twist. (N must be a multiple of 8 and the theories are modular invariant if it is a multiple of 24.) Similarly, from a doubly-even self-dual binary code C,

L. Dolan; P. Goddard; P. Montague

1990-01-01

322

On the vacuum state in quantum field theory. II

We want to construct, for every local irreducible quantum field theory which fulfils the spectrum condition, a new theory with the properties:1)It is physically equivalent to the given theory (in the sense ofHaag andKastler).2)The representation space contains a vacuum state.3)The new theory satisfies the spectrum condition.4)For every bounded region\\u000a

H.-J. Borchers

1965-01-01

323

Effective field theories for topological insulators by functional bosonization

NASA Astrophysics Data System (ADS)

Effective field theories that describe the dynamics of electric current for topological insulators in general dimension D = d+1 are discussed using the functional bosonization. For non-interacting topological insulators with a conserved U(1) charge and characterized by an integer topological invariant, we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the Axion term (when D is even). For topological insulators characterized by a Z2 topological invariant, their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for non- interacting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect, the putative ``fractional'' topological insulators and their possible effective field theories.

Chan, Pak On; Hughes, Taylor L.; Ryu, Shinsei; Fradkin, Eduardo

2013-03-01

324

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

325

String field theory at large B-field and noncommutative geometry

In the search for the exact minimum of the tachyon potential in the Witten's cubic string field theory we try to learn as much as possible from the string field theory in the large B-field background. We offer a simple alternative proof of the Witten's factorization, carry out the analysis of string field equations also for the non-commutative torus and

Martin Schnabl

2000-01-01

326

Strong field gravitational lensing in scalar tensor theories

NASA Astrophysics Data System (ADS)

Strong field gravitational lensing in the Brans Dicke scalar tensor theory has been studied. The deflection angle for photons passing very close to the photon sphere is estimated for the static spherically symmetric spacetime of the theory and the position and magnification of the relativistic images are obtained. Modelling the super massive central object of the galaxy by the Brans Dicke spacetime, numerical values of different strong lensing observables are estimated. It is found that against the expectation there is no significant scalar field effect on the strong field observable lensing parameters. This result raises question on the potentiality of strong field lensing to discriminate different gravitational theories.

Sarkar, Kabita; Bhadra, Arunava

2006-11-01

327

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

328

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

329

Dirac Structures and Implicit Lagrangian Systems in Electric Networks

In this paper, we apply Dirac structures and the associated theory of implicit Lagrangian systems to electric networks. We show how a Dirac structure on the flux linkage phase space can be induced from a KCL (Kirchhoff Current Law) constraint distribution on a configuration charge space in analogy with mechanics. In this context, a notion of implicit port-controlled Lagrangian systems

Hiroaki Yoshimura; Jerrold E. Marsden

330

String Theory - Nomological Unification and the Epicycles of the Quantum Field Theory Paradigm

String Theory is the result of the conjunction of three conceptually independent elements: (i) the metaphysical idea of a nomological unity of the forces, (ii) the model-theoretical paradigm of Quantum Field Theory, and (iii) the conflict resulting from classical gravity in a quantum world. String Theory is sometimes assumed to solve this conflict: by means of an application of the

Reiner Hedrich

2011-01-01

331

Pilot-wave approaches to quantum field theory

NASA Astrophysics Data System (ADS)

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 deBroglie 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.

Struyve, Ward

2011-07-01

332

Duality in scalar field theory on noncommutative phase spaces

We describe a novel duality symmetry of ?2n4-theory defined on noncommutative Euclidean space and with noncommuting momentum coordinates. This duality acts on the fields by Fourier transformation and scaling. It is an extension, to interactions defined with a star-product, of that which arises in quantum field theories of non-interacting scalar particles coupled to a constant background electromagnetic field. The dual

Edwin Langmann; Richard J. Szabo

2002-01-01

333

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

334

NASA Astrophysics Data System (ADS)

The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of new Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in a real-time setting for the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and {later a major hurricane.

Rutherford, B.; Montgomery, M. T.

2012-12-01

335

NASA Astrophysics Data System (ADS)

The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.

Rutherford, B.; Montgomery, M. T.

2012-12-01

336

NASA Astrophysics Data System (ADS)

The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of new Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed objectively. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics developed here are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.

Rutherford, B.; Montgomery, M. T.

2011-12-01

337

Perturbative Aspects of Low-Dimensional Quantum Field Theory

We investigate the low-dimensional applications of Quantum Field Theory (QFT), namely Chern-Simons-Witten Theory (CSWT) and Affine Toda Field Theory (ATFT) in 3- and 2- dimensions. We discuss the perturbative aspects of both theories and compare the results to the exact solutions obtained nonperturbatively. For the three dimensions CSWT case, the perturbative term agree with the nonperturbative polynomial invariants up to third order of the coupling constant 1/k. In the two dimensions ATFT, we investigate the perturbative aspect of S-matrices for A{sub 1}{sup (1)} case in eighth order of the coupling constant {beta}.

Wardaya, Asep Y. [Department of Physics, Diponegoro University, Jl. Prof. Soedarto SH, Semarang (Indonesia); Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, FMIPA, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132 (Indonesia); Zen, Freddy P.; Kosasih, Jusak S.; , Triyanta; Hartanto, Andreas [Indonesia Center for Theoretical and Mathematical Physics (ICTMP) (Indonesia); Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, FMIPA, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132 (Indonesia)

2010-06-22

338

Heavy Quarks, QCD, and Effective Field Theory

The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E#11;ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e#11;ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi#12;eld theoretic de#12;nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.

Thomas Mehen

2012-10-09

339

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

340

We propose a reformulation of Yang-Mills theory as a perturbative deformation of a novel topological (quantum) field theory. We prove that this reformulation of four-dimensional QCD leads to quark confinement in the sense of an area law of the Wilson loop. First, Yang-Mills theory with a non-Abelian gauge group G is reformulated as a deformation of a novel topological field

Kei-Ichi Kondo

1998-01-01

341

On revolutionizing quantum field theory with Tomita’s modular theory

In the book of Haag [Local Quantum Physics (Springer Verlag, Berlin, 1992)] about local quantum field theory the main results are obtained by the older methods of C*- and W*-algebra theory. A great advance, especially in the theory of W*-algebras, is due to Tomita’s discovery of the theory of modular Hilbert algebras [Quasi-standard von Neumann algebras, Preprint (1967)]. Because of

H. J. Borchers

2000-01-01

342

Semiclassical theory of unimolecular dissociation induced by a laser field

NASA Technical Reports Server (NTRS)

A semiclassical nonperturbative theory of direct photodissociation in a laser field is developed in which photon absorption and dissociation are treated in a unified fashion. This is achieved by visualizing nuclear dynamics as a representative particle moving on electronic-field surfaces. Methods are described for calculating dissociation rates and probabilities by Monte Carlo selection of initial conditions and integration of classical trajectories on these surfaces. This unified theory reduces to the golden rule expression in the weak-field and short-time limits, and predicts nonlinear behavior, i.e., breakdown of the golden rule expression in intense fields. Field strengths above which lowest-order perturbation theory fails to work have been estimated for some systems. Useful physical insights provided by the electronic-field representation have been illustrated. Intense field effects are discussed which are amenable to experimental observation. The semiclassical methods used here are also applicable to multiple-surface dynamics in fieldfree unimolecular and bimolecular reactions.

Yuan, J.-M.; George, T. F.

1978-01-01

343

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

344

Holomorphic anomalies in topological field theories

We study the stringy genus-one partition function of N = 2 SCFTs. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limit of this partition function yields the partition function of topological theory coupled to topological gravity. As an application we compute the number of holomorphic elliptic

M. Bershadsky; S. Cecotti; H. Ooguri; C. Vafa; S. Katz

1993-01-01

345

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

346

Field theory of the interacting string: The closed string

We recast dual models in the language of a quantum field theory of functional fields, restricting ourselves for simplicity to the closed string model. We derive the dynamics for both scalar and spinor functional fields from a unique parametrization invariant action. Passages to the Hamiltonian formalism and second quantization are explicitly worked out for the closed mesonic string in the

Charles Marshall; P. Ramond

1975-01-01

347

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

348

Tachyon condensation in large magnetic fields with background independent string field theory

We discuss the problem of tachyon condensation in the framework of background independent open string field theory. We show, in particular, that the computation of the string field theory action simplifies considerably if one looks at closed string backgrounds with a large Bab field, and can be carried out exactly for a generic tachyon profile. We confirm previous results on

Lorenzo Cornalba; Ecole Normale Superieure

2001-01-01

349

Neutrinoproduction of photons and pions from nucleons in a chiral effective field theory for nuclei

NASA Astrophysics Data System (ADS)

Neutrino-induced production (neutrinoproduction) of photons and pions from nucleons and nuclei is important for the interpretation of neutrino-oscillation experiments, as these photons and pions are potential backgrounds in the MiniBooNE experiment [A. A. Aquilar-Arevalo (MiniBooNE Collaboration), Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.100.032301 100, 032301 (2008)]. These processes are studied at intermediate energies, where the ?(1232) resonance becomes important. The Lorentz-covariant effective field theory, which is the framework used in this series of studies, contains nucleons, pions, ?s, isoscalar scalar (?) and vector (?) fields, and isovector vector (?) fields. The Lagrangian exhibits a nonlinear realization of (approximate) SU(2)L?SU(2)R chiral symmetry and incorporates vector meson dominance. In this paper, we focus on setting up the framework. Power counting for vertices and Feynman diagrams is explained. Because of the built-in symmetries, the vector current is automatically conserved, and the axial-vector current is partially conserved. To calibrate the axial-vector transition current (N??), pion production from the nucleon is used as a benchmark and compared to bubble-chamber data from Argonne and Brookhaven National Laboratories. At low energies, the convergence of our power-counting scheme is investigated, and next-to-leading-order tree-level corrections are found to be small.

Serot, Brian D.; Zhang, Xilin

2012-07-01

350

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

351

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

352

Noninteraction of Waves in Two-dimensional Conformal Field Theory

NASA Astrophysics Data System (ADS)

In higher dimensional quantum field theory, irreducible representations of the Poincaré group are associated with particles. Their counterpart in two-dimensional massless models are "waves" introduced by Buchholz. In this paper we show that waves do not interact in two-dimensional Möbius covariant theories and in- and out-asymptotic fields coincide. We identify the set of the collision states of waves with the subspace generated by the chiral components of the Möbius covariant net from the vacuum. It is also shown that Bisognano-Wichmann property, dilation covariance and asymptotic completeness (with respect to waves) imply Möbius symmetry. Under natural assumptions, we observe that the maps which give asymptotic fields in Poincaré covariant theory are conditional expectations between appropriate algebras. We show that a two-dimensional massless theory is asymptotically complete and noninteracting if and only if it is a chiral Möbius covariant theory.

Tanimoto, Yoh

2012-09-01

353

Bosonization in Higher Dimensions via Noncommutative Field Theory

We propose the bosonization of a many-body fermion theory in D spatial dimensions through a noncommutative field theory on a (2D-1)-dimensional space. This theory leads to a chiral current algebra over the noncommutative space and reproduces the correct perturbative Hilbert space and excitation energies for the fermions. The validity of the method is demonstrated by bosonizing a two-dimensional gas of fermions in a harmonic trap.

Polychronakos, Alexios P. [Physics Department, City College of the CUNY, New York, New York 10031 (United States)

2006-05-12

354

Bosonization in higher dimensions via noncommutative field theory.

We propose the bosonization of a many-body fermion theory in D spatial dimensions through a noncommutative field theory on a (2D-1)-dimensional space. This theory leads to a chiral current algebra over the noncommutative space and reproduces the correct perturbative Hilbert space and excitation energies for the fermions. The validity of the method is demonstrated by bosonizing a two-dimensional gas of fermions in a harmonic trap. PMID:16712379

Polychronakos, Alexios P

2006-05-12

355

Non-Associative Gauge Field Theories

NASA Astrophysics Data System (ADS)

The present contribution here is intended to settle down the basic ideas for a future work concerning the Dirac equation formulated in terms of octonions when the Cayley-Dickson construction is used to build this algebra. A description of octonions and an application of them to Yang-Mills theories is made following the previous work of O. K. Kalashinikov et. al. and S. Okubo.

Martínez-Merino, Aldo A.; Moreno, Guillermo

2006-01-01

356

A Mean Field Theory of Nonlinear Filtering

Abstract: We present a mean,eld particle theory for the numerical approx- imation of Feynman-Kac path integrals in the context of nonlinear,ltering. We show that the conditional distribution of the signal paths given a series of noisy and partial observation data is approximated by the occupation mea- sure of a genealogical tree model associated with mean,eld interacting particle model. The complete

Pierre Del Moral; Frédéric Patras; Sylvain Rubenthaler

2008-01-01

357

Localization and Dualities in Three-dimensional Superconformal Field Theories

NASA Astrophysics Data System (ADS)

In this thesis we apply the technique of localization to three-dimensional N = 2 superconformal field theories. We consider both theories which are exactly superconformal, and those which are believed to flow to nontrivial superconformal fixed points, for which we consider implicitly these fixed points. We find that in such theories, the partition function and certain supersymmetric observables, such as Wilson loops, can be computed exactly by a matrix model. This matrix model consists of an integral over g , the Lie algebra of the gauge group of the theory, of a certain product of 1-loop factors and classical contributions. One can also consider a space of supersymmetric deformations of the partition function corresponding to the set of abelian global symmetries. In the second part of the thesis we apply these results to test dualities. We start with the case of ABJM theory, which is dual to M-theory on an asymptotically AdS4 x S7 background. We extract strong coupling results in the field theory, which can be compared to semiclassical, weak coupling results in the gravity theory, and a nontrivial agreement is found. We also consider several classes of dualities between two three-dimensional field theories, namely, 3D mirror symmetry, Aharony duality, and Giveon-Kutasov duality. Here the dualities are typically between the IR limits of two Yang-Mills theories, which are strongly coupled in three dimensions since Yang-Mills theory is asymptotically free here. Thus the comparison is again very nontrivial, and relies on the exactness of the localization computation. We also compare the deformed partition functions, which tests the mapping of global symmetries of the dual theories. Finally, we discuss some recent progress in the understanding of general three-dimensional theories in the form of the F-theorem, a conjectured analogy to the a-theorem in four dimensions and c-theorem in two dimensions, which is closely related to the localization computation.

Willett, Brian

358

Advances in reversed field pinch theory and computation

Advances in theory and computations related to the reversed field pinch (RFP) are presented. These are: (1) the effect of the dynamo on thermal transport; (2) a theory of ion heating due to dynamo fluctuations; (3) studies of active and passive feedback schemes for controlling dynamo fluctuations; and (4) an analytic model for coupled g-mode and rippling turbulence in the RFP edge.

Schnack, D.D.; Ho, Y.L. [Science Applications International Corp., San Diego, CA (United States); Carreras, B.A.; Sidikman, K. [Oak Ridge National Lab., TN (United States); Craddock, G.G.; Mattor, N. [Lawrence Livermore National Lab., CA (United States); Nebel, R.A. [Los Alamos National Lab., NM (United States); Prager, S.C.; Terry, P.W.; Zita, E.J. [Univ. of Wisconsin, Madison, WI (United States). Dept. of Physics

1992-12-31

359

Conformal Field Theory and Its Application to Strings.

National Technical Information Service (NTIS)

Conformal field theories on Riemann surfaces are considered and the result is applied to study the loop amplitudes for bosonic strings. It is shown that there is a close resemblance between the loop amplitudes for phi/sup 3/-theory and the expressions for...

E. P. Verlinde

1988-01-01

360

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

361

A Leading Log Approximation for Inflationary Quantum Field Theory

NASA Astrophysics Data System (ADS)

During inflation explicit perturbative computations of quantum field theories which contain massless, non-conformal fields exhibit secular effects that grow as powers of the logarithm of the inflationary scale factor. Starobinski??'s technique of stochastic inflation not only reproduces the leading infrared logarithms at each order in perturbation theory, it can sometimes be summed to reveal what happens when inflation has proceeded so long that the large logarithms overwhelm even very small coupling constants. It is thus a cosmological analogue of what the renormalization group does for the ultraviolet logarithms of quantum field theory, and generalizing this technique to quantum gravity is a problem of great importance. There are two significant differences between gravity and the scalar models for which stochastic formulations have so far been given: derivative interactions and the presence of constrained fields. We use explicit perturbative computations in two simple scalar models to infer a set of rules for stochastically formulating theories with these features.

Woodard, R. P.

2005-11-01

362

Field Theory Anomalies Involving the Energy-Momentum Tensor.

National Technical Information Service (NTIS)

Generalized Ward-Takahashi identities (WTI's) of the energy--momentum tensor in a free spinor field theory with SU(3) currents were analyzed for possible noncanonical behavior (anomalies). The WTI's, derived by a functional integration technique, are the ...

D. B. Zacrep

1975-01-01

363

String Field Theory Vertices for Fermions of Integral Weight

NASA Astrophysics Data System (ADS)

We construct Witten-type string field theory vertices for a fermionic first order system with conformal weights (0,1) in the operator formulation using delta-function overlap conditions as well as the Neumann function method. The identity, the reflector and the interaction vertex are treated in detail paying attention to the zero mode conditions and the U(1) charge anomaly. The Neumann coefficients for the interaction vertex are shown to be intimately connected with the coefficients for bosons allowing a simple proof that the reparametrization anomaly of the fermionic first order system cancels the contribution of two real bosons. This agrees with their contribution c = -2 to the central charge. The overlap equations for the interaction vertex are shown to hold. Our results have applications in N = 2 string field theory, Berkovits' hybrid formalism for superstring field theory, the etaxi-system and the twisted bc-system used in bosonic vacuum string field theory.

Kling, Alexander; Uhlmann, Sebastian

2003-07-01

364

Mutual information after a local quench in conformal field theory

NASA Astrophysics Data System (ADS)

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 formulas 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.

Asplund, Curtis T.; Bernamonti, Alice

2014-03-01

365

Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry

Gyrokinetic theory is based on an asymptotic expansion in the small parameter\\u000a$\\\\epsilon$, defined as the ratio of the gyroradius and the characteristic\\u000alength of variation of the magnetic field. In this article, this ordering is\\u000astrictly implemented to compute the electrostatic gyrokinetic phase-space\\u000aLagrangian in general magnetic geometry to order $\\\\epsilon^2$. In particular, a\\u000anew expression for the complete

Felix I. Parra; Ivan Calvo

2010-01-01

366

Diffusion and Brownian motion in Lagrangian coordinates.

In this paper we consider the convection-diffusion problem of a passive scalar in Lagrangian coordinates, i.e., in a coordinate system fixed on fluid particles. Both the convection-diffusion partial differential equation and the Langevin equation are expressed in Lagrangian coordinates and are shown to be equivalent for uniform, isotropic diffusion. The Lagrangian diffusivity is proportional to the square of the relative change of surface area and is related to the Eulerian diffusivity through the deformation gradient tensor. Associated with the initial value problem, we relate the Eulerian to the Lagrangian effective diffusivities (net spreading), validate the relation for the case of linear flow fields, and infer a relation for general flow fields. Associated with the boundary value problem, if the scalar transport problem possesses a time-independent solution in Lagrangian coordinates and the boundary conditions are prescribed on a material surface/interface, then the net mass transport is proportional to the diffusion coefficient. This can be also shown to be true for large Peclet number and time-periodic flow fields, i.e., closed pathlines. This agrees with results for heat transfer at high Peclet numbers across closed streamlines. PMID:17477617

Fyrillas, Marios M; Nomura, Keiko K

2007-04-28

367

The flux-rope-fibre theory of solar magnetic fields

The flux-rope theory of solar magnetic fields and their effects is reviewed. The traditional theory of emerging magnetic flux is discussed, emphasizing kinematic considerations, dynamic effects, and various difficulties with the traditional concepts. Evidence in favor of the flux-rope-fiber model of solar magnetic fields is examined, including observations of magnetic structures in growing active regions, sunspots and spot groups, fine

J. H. Piddington

1978-01-01

368

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

369

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

370

Classical effective field theory for weak ultra relativistic scattering

Inspired by the problem of Planckian scattering we describea classical effective field theory for weak ultra relativistic\\u000a scattering in which field propagation is instantaneous and transverse and the particles’ equations of motion localize to the\\u000a instant of passing. An analogy with the non-relativistic (post-Newtonian) approximation is stressed. The small parameter is\\u000a identified and power counting rules are established. The theory

Barak Kol

2011-01-01

371

Non-perturbative methods in relativistic field theory

This talk reviews relativistic methods used to compute bound and low energy scattering states in field theory, with emphasis on approaches that John Tjon and I discussed (and argued about) together. I compare the Bethe–Salpeter and Covariant Spectator equations, show some applications, and then report on some of the things we have learned from the beautiful Feynman–Schwinger technique for calculating the exact sum of all ladder and crossed ladder diagrams in field theory.

Franz Gross

2013-03-01

372

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

373

Random Tilings of High Symmetry: I. Mean-Field Theory

NASA Astrophysics Data System (ADS)

We study random tiling models in the limit of high rotational symmetry. In this limit a mean-field theory yields reasonable predictions for the configurational entropy of free boundary rhombus tilings in two dimensions. We base our mean-field theory on an iterative tiling construction inspired by the work of de Bruijn. In addition to the entropy, we consider correlation functions, phason elasticity and the thermodynamic limit. Tilings of dimension other than two are considered briefly.

Destainville, N.; Widom, M.; Mosseri, R.; Bailly, F.

2005-09-01

374

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.

Andreanov, Alexei; Lefevre, Alexandre [Service de Physique Theorique, Orme des Merisiers-CEA Saclay, 91191 Gif sur Yvette Cedex (France); Biroli, Giulio [Service de Physique de l'Etat Condense, Orme des Merisiers-CEA Saclay, 91191 Gif sur Yvette Cedex (France); Bouchaud, Jean-Philippe [Service de Physique de l'Etat Condense, Orme des Merisiers-CEA Saclay, 91191 Gif sur Yvette Cedex (France); Science and Finance, Capital Fund Management, 6 Boulevard Haussmann, 75009 Paris (France)

2006-09-15

375

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

376

NASA Technical Reports Server (NTRS)

A 3-D finite element program capable of simulating the dynamic behavior in the vicinity of the impact point, together with predicting the dynamic response in the remaining part of the structural component subjected to high velocity impact is discussed. The finite algorithm is formulated in a general moving coordinate system. In the vicinity of the impact point contained by a moving failure front, the relative velocity of the coordinate system will approach the material particle velocity. The dynamic behavior inside the region is described by Eulerian formulation based on a hydroelasto-viscoplastic model. The failure front which can be regarded as the boundary of the impact zone is described by a transition layer. The layer changes the representation from the Eulerian mode to the Lagrangian mode outside the failure front by varying the relative velocity of the coordinate system to zero. The dynamic response in the remaining part of the structure described by the Lagrangian formulation is treated using advanced structural analysis. An interfacing algorithm for coupling CELFE with NASTRAN is constructed to provide computational capabilities for large structures.

Lee, C. H.

1978-01-01

377

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

378

Statistical field theories deformed within different calculi

. \\u000a Within the framework of basic-deformed and finite-difference calculi,\\u000a as well as deformation procedures proposed by Tsallis, Abe, and Kaniadakis and\\u000a generalized by Naudts, we develop field-theoretical schemes of statistically\\u000a distributed fields. We construct a set of generating functionals and find their\\u000a connection with corresponding correlators for basic-deformed,\\u000a finite-difference, and Kaniadakis calculi. Moreover, we introduce pair of\\u000a additive functionals, which

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

2010-01-01

379

Accretion disks and dynamos: toward a unified mean field theory

NASA Astrophysics Data System (ADS)

Conversion of gravitational energy into radiation near stars and compact objects in accretion disks and the origin of large-scale magnetic fields in astrophysical rotators have often been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large-scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disk theory have exemplified such ongoing pursuits. Twenty-first century MFD theory has more nonlinear predictive power compared to 20th century MFD theory, whereas alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory are applicable to accretion theory and the two are really artificially separated pieces of what should ultimately be a single coupled theory. I discuss pieces of progress that provide clues toward a unified theory. A key concept is that large-scale magnetic fields can be sustained via local or global magnetic helicity fluxes or via relaxation of small-scale magnetic fluctuations, without appealing to the traditional kinetic helicity driver of 20th century textbooks. These concepts may help explain the formation of large-scale fields that supply non-local angular momentum transport via coronae and jets in a unified theory of accretion and dynamos. In diagnosing the role of helicities and helicity fluxes in disk simulations, it is important to study each disk hemisphere separately to avoid being potentially misled by the cancelation that occurs as a result of reflection asymmetry. The fraction of helical field energy in disks is expected to be small compared to the total field in each hemisphere as a result of shear, but can still play a fundamental role in large-scale dynamo action.

Blackman, Eric G.

2012-11-01

380

NASA Technical Reports Server (NTRS)

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Liou, Meng-Sing

1992-01-01

381

Gauge invariant field theory of free strings

We present the gauge invariant and covariant equations of motion for free strings and superstrings, using a simple method of successive gauge transformations. Gauge invariance is enforced by introducing both subsidiary and Stueckelberg fields. We use methods of cohomology associated with the various Virasoro algebras, and derive the cohomology algebras associated with the boson and fermion sector of the open

D. Pfeffer; P. Ramond; V. G. J. Rodgers

1986-01-01

382

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

383

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

384

Axisymmetric stationary vacuum fields in the general scalar tensor theory

NASA Astrophysics Data System (ADS)

The highly nonlinear field equations of the general scalar-tensor (ST) theory of gravitation of Nordvedt (1970) are investigated analytically. A method is developed to obtain solutions of the stationary axially symmetric (AS) vacuum fields of ST theory from either a stationary AS solution of the Einstein vacuum equation or the AS static ST vacuum fields. The ST analogs of the solutions of Kerr (1963) are derived as an example, and the applicability of the method to the solutions of Tomimatsu and Sato (1973), Yamazaki (1976), and Kinnersley and Chitre (1978) is indicated. The results given represent a generalization of the analysis of Nayak and Tiwari (1977) in Brans-Dicke theory to the general ST theory.

Singh, T.; Singh, T.

1984-03-01

385

Long-range interactions in lattice field theory

Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.

Rabin, J.M.

1981-06-01

386

Conformal field theory of Painlevé VI

NASA Astrophysics Data System (ADS)

Generic Painlevé VI tau function ? ( t) can be interpreted as four-point correlator of primary fields of arbitrary dimensions in 2D CFT with c = 1. Using AGT combinatorial representation of conformal blocks and determining the corresponding structure constants, we obtain full and completely explicit expansion of ? ( t) near the singular points. After a check of this expansion, we discuss examples of conformal blocks arising from Riccati, Picard, Chazy and algebraic solutions of Painlevé VI.

Gamayun, O.; Iorgov, N.; Lisovyy, O.

2012-10-01

387

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

388

A new rolling tachyon solution of cubic string field theory

We present a new analytic time dependent solution of cubic string field theory at the lowest order in the level truncation scheme. The tachyon profile we have found is a bounce in time, a C? function which represents an almost exact solution, with an extremely good degree of accuracy, of the classical equations of motion of the truncated string field

Valentina Forini; Gianluca Grignani; Giuseppe Nardelli

2005-01-01

389

Novel collective excitations in a hot scalar field theory

NASA Astrophysics Data System (ADS)

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.

Drewes, Marco

2014-05-01

390

Mean field theory of self-organized critical phenomena

A mean field theory is presented for the recently discovered self-organized critical phenomena. The critical exponents are calculated and found to be the same as the mean field values for percolation. The power spectrum has 1/f behavior with exponent Phi = 1.

Tang, C.; Bak, P.

1988-06-01

391

Analytic solution for tachyon condensation in open string field theory

We propose a new basis in Witten's open string field theory, in which the star product simplifies considerably. For a convenient choice of gauge the classical string field equation of motion yields straightforwardly an exact analytic solution that represents the nonperturbative tachyon vacuum. The solution is given in terms of Bernoulli numbers and the equation of motion can be viewed

Martin Schnabl

2005-01-01

392

Zero point energies in light cone field theory

In this paper, we study the role of zero point energies in light front quantized field theories using a simple scalar field model with quartic coupling. In the equal time formalism, the zero point energies are renormalized by normal ordering with respect to some vacuum state, which is varied to determine the true, interacting vacuum. On the light front, we

C. J. Benesh; J. P. Vary

1991-01-01

393

De Donder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory

A quantization of field theory based on the De Donder-Weyl (DW) covariant Hamiltonian formulation is discussed. A hypercomplex extension of quantum mechanics, in which the space-time Clifford algebra replaces that of the complex numbers, appears as a result of quantization of Poisson brackets on differential forms which were put forward for the DW theory earlier. The proposed covariant hypercomplex Schrödinger

Igor V. Kanatchikov

1999-01-01

394

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

395

Phase diagram of N = 2 superconformal field theories and bifurcation sets in catastrophe theory.

National Technical Information Service (NTIS)

Phase diagrams of N=2 superconformal field theories are mapped out. It is shown that they coincide with bifurcation sets in catastrophe theory. The results are applied to the determination of renormalization group flows triggered by a combination of two o...

Kei Ito

1989-01-01

396

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

NASA Astrophysics Data System (ADS)

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.

Cardoso, Vitor; Porto, Rafael A.

2014-05-01

397

The objective of this project was to predict the yield of a reactor operated under turbulent flow conditions with a Newtonian liquid in which reagents and products have been dissolved. There are no restrictions on the complexity of reactions. To predict the results of coupled reactions the approach chosen for modelling is a Lagrangian description of reaction zones in a

R. A. Bakker

1996-01-01

398

Lagrangian Meshfree Formulation for Analysis of Geotechnical Materials

A Lagrangian reproducing kernel formulation is introduced as an approximation of field variables under the Galerkin meshfree framework of geomechanics. The reproducing kernel approximation is formulated with reference to the material coordinates, yielding an approach that is applicable to both total and updated Lagrangian formulations. In the method presented, geotechnical materials described by pressure-sensitive mul- tisurface plasticity with a cap

Cheng-Tang Wu; Jiun-Shyan Chen; Liqun Chi; Frank Huck

2001-01-01

399

Modeling pollutant transport using a meshless-lagrangian particle model

A combined meshless-Lagrangian particle transport model is used to predict pollutant transport over irregular terrain. The numerical model for initializing the velocity field is based on a meshless approach utilizing multiquadrics established by Kansa. The Lagrangian particle transport technique uses a random walk procedure to depict the advection and dispersion of pollutants over any type of surface, including street and city canyons

Carrington, D. B. (David B.); Pepper, D. W. (Darrell W.)

2002-01-01

400

Cold Atom Simulation of Interacting Relativistic Quantum Field Theories

NASA Astrophysics Data System (ADS)

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.

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

2010-11-01

401

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. PMID:21231152

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

2010-11-01

402

Stueckelberg's Unitary Field Theory of 1936-1939

NASA Astrophysics Data System (ADS)

The scientific production of Ernst Carl Gerlach Stueckelberg von Breidenbach reached a peak in the years 1936-39, in which he produced a series of deeply original papers on quantum field theory and its applications to nuclear matter. The only trace of this work in the memory of today's physicists is the Stueckelberg B-field, a trick to avoid troubles in quantizing massive vector-fields. Yet Stueckelberg's innovations went far beyond this formal contribution. For instance, he devised the first manifestly covariant perturbation theory, and he greatly contributed to the meson-field theory of nuclear interactions. Considerations of style, timing, and character explain the disparity between his achievements and their long-term appreciation.

Darrigol, Olivier

403

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

NASA Astrophysics Data System (ADS)

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3 part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.

Asano, Masako

2013-03-01

404

Renormalization and non-linear symmetries in quantum field theory

NASA Astrophysics Data System (ADS)

Most of the phenomena we experience, from the microscopic world to the universe at its largest scales, are out of equilibrium and their comprehensive formalization is one of the open problems in theoretical physics. Fluids of interacting particles cooled down or compressed quickly enough to become amorphous solids are an example of rich out-of-equilibrium systems with very slow relaxation dynamics. Even though the equilibrium phases are ordered, these systems remain trapped in glassy metastable states, with disordered microscopic structures. As a realistic model of this phenomenology, in the first part of this work I focused on a field theory of particles obeying a Brownian dynamics. The field-theoretic action displays a time-reversal symmetry leading to Fluctuation-Dissipation relations. For non-interacting particles I solved the field theory exactly, providing the explicit form of all the correlation functions, with their space and time dependence. As a non-perturbative result, the distribution of the density field has been proven to be Poissonian and not Gaussian. For interacting particles the field theory presents two major challenges: its apparent non-renormalizability and a non-linear implementation of the time-reversal symmetry. Non-linear field redefinitions can be used to make the symmetry linear and might even lead to the solution of the interacting equations of motion. However they also alter the renormalizability properties of a field theory. These challenges inspired the second part of the work, where a more abstract approach was taken. Using algebraic methods I investigated the effect of non-linear field redefinitions both on symmetry and on renormalization by focusing on simple scalar field theories as toy models. In the formal setting of the Hopf algebra of Feynman diagrams, symmetries take the form of Hopf ideals and enforce relations among scattering amplitudes; such relations can drastically reduce the number of independent couplings in a field theory, in some cases providing a key to renormalize theories which appear to be non-renormalizable by powercounting. Explicit results for the toy field theories have been obtained by computing the residues of hundreds of thousands of loop integrals with a symbolic computational tool I developed.

Velenich, Andrea

405

Symmetries in Lagrangian Dynamics

ERIC Educational Resources Information Center

In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…

Ferrario, Carlo; Passerini, Arianna

2007-01-01

406

Effective field theories for topological insulators by functional bosonization

NASA Astrophysics Data System (ADS)

Effective field theories that describe the dynamics of a conserved U(1) current in terms of “hydrodynamic” degrees of freedom of topological phases in condensed matter are discussed in general dimension D=d+1 using the functional bosonization technique. For noninteracting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII), and in the “primary series” of topological insulators, in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the ? (when D is even) terms. For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative “fractional” topological insulators and their possible effective field theories, and use them to determine the physical properties of these nontrivial quantum phases.

Chan, AtMa; Hughes, Taylor L.; Ryu, Shinsei; Fradkin, Eduardo

2013-02-01

407

Local covariant quantum field theory over spectral geometries

NASA Astrophysics Data System (ADS)

A framework which combines ideas from Connes' noncommutative geometry, or spectral geometry, with recent ideas on generally covariant quantum field theory, is proposed in the present work. A certain type of spectral geometries modelling (possibly noncommutative) globally hyperbolic spacetimes is introduced in terms of the so-called globally hyperbolic spectral triples. The concept is further generalized to a category of globally hyperbolic spectral geometries whose morphisms describe the generalization of isometric embeddings. Then a local generally covariant quantum field theory is introduced as a covariant functor between such a category of globally hyperbolic spectral geometries and the category of involutive algebras (or *-algebras). Thus, a local covariant quantum field theory over spectral geometries assigns quantum fields not just to a single noncommutative geometry (or noncommutative spacetime), but simultaneously to 'all' spectral geometries, while respecting the covariance principle demanding that quantum field theories over isomorphic spectral geometries should also be isomorphic. It is suggested that in a quantum theory of gravity a particular class of globally hyperbolic spectral geometries is selected through a dynamical coupling of geometry and matter compatible with the covariance principle.

Paschke, Mario; Verch, Rainer

2004-12-01

408

Numerical coarse-graining of fluid field theories

NASA Astrophysics Data System (ADS)

We present a formalism for the systematic numerical coarse-graining of field-theoretic models of fluids that draws upon techniques from both the Monte Carlo renormalization group and particle-based coarse-graining literature. A force-matching technique initially developed for coarse-graining particle-based interaction potentials is adapted to calculate renormalized field-theoretic coupling coefficients in a complex-valued field theory, and a related method is introduced for coarse-graining field-theoretic operators. The viability of this methodology is demonstrated by coarse-graining a field-theoretic model of a Gaussian-core fluid and thereby reducing lattice discretization errors.

Villet, Michael C.; Fredrickson, Glenn H.

2010-01-01

409

A relativistically covariant version of Bohm's quantum field theory for the scalar field

NASA Astrophysics Data System (ADS)

We give a relativistically covariant, wave-functional formulation of Bohm's quantum field theory for the scalar field based on a general foliation of spacetime by space-like hypersurfaces. The wave functional, which guides the evolution of the field, is spacetime-foliation independent but the field itself is not. Hence, in order to have a theory in which the field may be considered a beable, some extra rule must be given to determine the foliation. We suggest one such rule based on the eigenvectors of the energy-momentum tensor of the field itself.

Horton, George; Dewdney, Chris

2004-12-01

410

Green's Functions Involving Gauge Transformed Field Variables

The technique of path integration is remarkably well suited for the calculation of scattering amplitudes in relativistic quantum field theories. However, for the case of a field theory which is defined by a Lagrangian density that is invariant under a set of local gauge transformations, the standard Feynman Path Integral is not adequate for the purpose of performing calculations. This

Stephen Blair Phillips

1985-01-01

411

Janus field theories from multiple M2 branes

Based on the recent proposal of N=8 superconformal gauge theories of the multiple M2 branes, we derive (2+1)-dimensional supersymmetric Janus field theories with a space-time dependent coupling constant. From the original Bagger-Lambert model, we get a supersymmetric field theory with a similar action to the N D2 branes, but the coupling varies with the space-time as a function of the light-cone coordinate, g(t+x). Half of the supersymmetries can be preserved. We further investigate the M2 brane action deformed by mass and Myers-like terms. In this case, the final Yang-Mills action is deformed by mass and Myers terms, and the coupling behaves as exp({mu}x) where {mu} is a constant mass parameter. Weak coupling gauge theory is continuously changed to strong coupling in the large x region.

Honma, Yoshinori; Iso, Satoshi; Sumitomo, Yoske; Zhang, Sen [Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK) and Department of Particles and Nuclear Physics, Graduate University for Advanced Studies (SOKENDAI), Oho 1-1, Tsukuba, Ibaraki 305-0801 (Japan)

2008-07-15

412

Non-Abelian fluid dynamics in Lagrangian formulation

NASA Astrophysics Data System (ADS)

Non-Abelian extensions of fluid dynamics, which can have applications to the quark-gluon plasma, are given. These theories are presented in a symplectic or Lagrangian formulation and involve a fluid generalization of the Kirillov-Kostant form well known in Lie group theory. In our simplest model the fluid flows with velocity v and, in the presence of non-Abelian chromoelectric or magnetic Ea/Ba fields, the fluid feels a Lorentz force of the form QaEa+(v/c)×QaBa, where Qa is a space-time local non-Abelian charge satisfying a fluid Wong equation [(Dt+v?D)Q]a=0 with gauge covariant derivatives.

Bistrovic, B.; Jackiw, R.; Li, H.; Nair, V. P.; Pi, S.-Y.

2003-01-01

413

A solvable toy model for tachyon condensation in string field theory

The lump solution of phi3 field theory provides a toy model for unstable D-branes of bosonic string theory. The field theory living on this lump is itself a cubic field theory involving a tachyon, two additional scalar fields, and a scalar field continuum. Its action can be written explicitly because the fluctuation spectrum of the lump turns out to be

Barton Zwiebach

2000-01-01

414

Quantum field theory constrains traversable wormhole geometries

Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty-principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable. {copyright} {ital 1996 The American Physical Society.}

Ford, L.H. [Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)] [Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155 (United States); Roman, T.A. [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155 (United States)] [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155 (United States); [Department of Physics and Earth Sciences, Central Connecticut State University, New Britain, Connecticut 06050 (United States)

1996-05-01

415

Noncommutative quantum mechanics from noncommutative quantum field theory.

We derive noncommutative multiparticle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Particles of opposite charges are found to have opposite noncommutativity. As a result, there is no noncommutative correction to the hydrogen atom spectrum at the tree level. We also comment on the obstacles to take noncommutative phenomenology seriously and propose a way to construct noncommutative SU(5) grand unified theory. PMID:11955188

Ho, Pei-Ming; Kao, Hsien-Chung

2002-04-15

416

Associative-algebraic approach to logarithmic conformal field theories

We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non-semisimple associative algebras appearing in their lattice regularizations (as discussed in a companion paper [N. Read, H. Saleur, Enlarged symmetry algebras of spin chains, loop models, and S-matrices, cond-mat\\/0701259]). Here we work out in detail two examples of theories derived

N. Read; Hubert Saleur

2007-01-01

417

Chiral Effective Field Theory in the ?-RESONANCE Region

NASA Astrophysics Data System (ADS)

I discuss the problem of constructing an effective low-energy theory in the vicinity of a resonance or a bound state. The focus is on the example of the ?(1232), the lightest resonance in the nucleon sector. Recent developments of the chiral effective-field theory in the ?-resonance region are briefly reviewed. I conclude with a comment on the merits of the manifestly covariant formulation of chiral EFT in the baryon sector.

Pascalutsa, Vladimir

2007-10-01

418

Supergravity, nonconformal field theories, and brane-worlds

We consider the supergravity dual descriptions of nonconformal super Yang-Mills theories realized on the world-volume of Dp-branes. We use the dual description to compute stress-energy tensor and current correlators. We apply the results to the study of dilatonic brane-worlds described by nonconformal field theories coupled to gravity. We find that brane-worlds based on D4- and D5-branes exhibit a localization of

Tony Gherghetta; Yaron Oz

2002-01-01

419

Local Commutators and Deformations in Conformal Chiral Quantum Field Theories

NASA Astrophysics Data System (ADS)

We study the general form of Möbius covariant local commutation relations in conformal chiral quantum field theories and show that they are intrinsically determined up to structure constants, which are subject to an infinite system of constraints. The deformation theory of these commutators is controlled by a cohomology complex, whose cochain spaces consist of linear maps that are subject to a complicated symmetry property, a generalization of the anti-symmetry of the Lie algebra case.

Kukhtina, Antonia M.; Rehren, Karl-Henning

420

Global Gauge Anomalies in Coset Models of Conformal Field Theory

NASA Astrophysics Data System (ADS)

We study the occurrence of global gauge anomalies in the coset models of two-dimensional conformal field theory that are based on gauged WZW models. A complete classification of the non-anomalous theories for a wide family of gauged rigid adjoint or twisted-adjoint symmetries of WZW models is achieved with the help of Dynkin's classification of Lie subalgebras of simple Lie algebras.

de Fromont, Paul; Gaw?dzki, Krzysztof; Tauber, Clément

2014-06-01

421

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

422

Quantum field theory in spaces with closed timelike curves

NASA Astrophysics Data System (ADS)

Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2?. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

Boulware, David G.

1992-11-01

423

The large N limit of superconformal field theories and supergravity

We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large N. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The 't Hooft limit of 3+1N=4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions.

Maldacena, Juan [Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138 (United States)

1999-07-13

424

Quantum field theory on a cosmological, quantum space-time

In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker space-times arise as well-defined approximations to specific quantum geometries. We initiate the development of a quantum theory of test scalar fields on these quantum geometries. Emphasis is on the new conceptual ingredients required in the transition from classical space-time backgrounds to quantum space-times. These include a ''relational time''a la Leibniz, the emergence of the Hamiltonian operator of the test field from the quantum constraint equation, and ramifications of the quantum fluctuations of the background geometry on the resulting dynamics. The familiar quantum field theory on classical Friedmann-LeMaitre-Robertson-Walker models arises as a well-defined reduction of this more fundamental theory.

Ashtekar, Abhay [Institute for Gravitation and the Cosmos and Physics Department, Penn State, University Park, Pennsylvania 16802 (United States); Kaminski, Wojciech; Lewandowski, Jerzy [Institute for Gravitation and the Cosmos and Physics Department, Penn State, University Park, Pennsylvania 16802 (United States); Instytut Fizyki Teoretycznej Uniwersytet Warszawski, ul.Hoza 69, PL-00 681 Warsaw (Poland)

2009-03-15

425

Quantum entanglement of local operators in conformal field theories.

We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles. PMID:24702348

Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi

2014-03-21

426

Light-like tachyon condensation in open string field theory

NASA Astrophysics Data System (ADS)

We use open string field theory to study the dynamics of unstable branes in the bosonic string theory, in the background of a generic linear dilaton. We find a simple exact solution describing a dynamical interpolation between the perturbative vacuum and the recently discovered nonperturbative tachyon vacuum. In our solution, the open string tachyon increases exponentially along a null direction, after which nonlinearities set in and cause the solution to asymptote to a static state. In particular, the wild oscillations of the open string fields which plague the time-like rolling tachyon solution are entirely absent. Our model thus represents the first example proving that the true tachyon vacuum of open string field theory can be realized as the endpoint of a dynamical transition from the perturbative vacuum.

Hellerman, Simeon; Schnabl, Martin

2013-04-01

427

Thermoelasticity and plasticity of composites -- I. Mean field theory

A simple mean field model leads to a new formulation of the theory of bounds for thermoelastic composites whose phase volume fractions are known, the theory expresses the equivalent transformation strain as the sum of a term proportional to the external stress and a term proportional to the inelastic strain misfit. Comparisons with selected experiments show that a realistic description of the plasticity of composites in general has to account for the effects of matrix constraint and elastic heterogeneity. The new formulation may be combined with a dislocation theory of constrained flow. Implications for cyclic plasticity are pointed out.

Pedersen, O.B.

1983-11-01

428

Theory of Atom-Metal Interaction. Ii. Perturbation Theory in Field Ionization Calculations.

National Technical Information Service (NTIS)

The use of the time-dependent perturbation theory is applied to the process of field ionization. When suitable approximations are made for the initial and final state wave functions, the probability of field ionization as a function of atom metal separati...

D. S. Boudreaux P. H. Cutler

1966-01-01

429

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

430

Weak gravity conjecture for effective field theories with N species

NASA Astrophysics Data System (ADS)

We conjecture an intrinsic UV cutoff for the validity of the effective field theory with a large number of species coupled to gravity. In four dimensions such an UV cutoff takes the form ?=?/NMp for N scalar fields with the same potential ??i4, i=1,…,N. This conjecture implies that the assisted chaotic inflation or N-flation might be in the swampland, not in the landscape. Similarly an UV cutoff ?=gMp/N is conjectured for the U(1) gauge theory with N species.

Huang, Qing-Guo

2008-05-01

431

Unification of General Relativity with Quantum Field Theory

NASA Astrophysics Data System (ADS)

In the frame of quantum field theory, instead of using the action principle, we deduce the Einstein equation from purely the general covariant principle and the homogeneity of spacetime. The Einstein equation is shown to be the gauge equation to guarantee the local symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field theory, only electroweak-strong interactions should be considered with the curved spacetime metric determined by the Einstein equation.

Ni, Jun

2011-11-01

432

Exact wave functions in a noncommutative field theory.

We consider the nonrelativistic field theory with a quartic interaction on a noncommutative plane and compute the 2-->2 scattering amplitude within perturbative analysis to all orders. We regain the results of the perturbative analysis by finding the scattering and the bound state wave functions of the two particle Schrodinger equation. These wave functions unusually have two center positions in the relative coordinates, whose separation is transverse to the total momentum and scales linearly with its magnitude, exhibiting the stringy nature of the noncommutative field theory. PMID:11019273

Bak, D; Kim, S K; Soh, K S; Yee, J H

2000-10-01

433

Negative contributions to S in an effective field theory

We show that an effective field theory that includes non-standard couplings between the electroweak gauge bosons and the top and bottom quarks may yield negative contributions to both the S and T oblique radiative electroweak parameters. We find that such an effective field theory provides a better fit to data than the standard model (the {chi}{sup 2} per degree of freedom is half as large). We examine in some detail an illustrative model where the exchange of heavy scalars produces the correct type of non-standard couplings.

Dobrescu, Bogdan A.; Terning, John

1997-09-19

434

A field theory of piezoelectric media containing dislocations

NASA Astrophysics Data System (ADS)

A field theory is proposed to extend the standard piezoelectric framework for linear elastic solids by accounting for the presence and motion of dislocation fields and assessing their impact on the piezoelectric properties. The proposed theory describes the incompatible lattice distortion and residual piezoelectric polarization fields induced by dislocation ensembles, as well as the dynamic evolution of these fields through dislocation motion driven by coupled electro-mechanical loading. It is suggested that (i) dislocation mobility may be enhanced or inhibited by the electric field, depending on the polarity of the latter, (ii) plasticity mediated by dislocation motion allows capturing long-term time-dependent properties of piezoelectric polarization. Due to the continuity of the proposed electro-mechanical framework, the stress/strain and polarization fields are smooth even in the dislocation core regions. The theory is applied to gallium nitride layers for validation. The piezoelectric polarization fields associated with bulk screw/edge dislocations are retrieved and surface potential modulations are predicted. The results are extended to dislocation loops.

Taupin, V.; Fressengeas, C.; Ventura, P.; Lebyodkin, M.; Gornakov, V.

2014-04-01

435

Coupled Mesh Lagrangian/ALE modeling: opportunities and challenges.

The success of Lagrangian contact modeling leads one to believe that important aspects of this capability may be used for multi-material modeling when only a portion of the simulation can be represented in a Lagrangian frame. We review current experience with two dual mesh technologies where one of these meshes is a Lagrangian mesh and the other is an Arbitrary Lagrangian/Eulerian (ALE) mesh. These methods are cast in the framework of an operator-split ALE algorithm where a Lagrangian step is followed by a remesh/remap step. An interface-coupled methodology is considered first. This technique is applicable to problems involving contact between materials of dissimilar compliance. The technique models the more compliant (soft) material as ALE while the less compliant (hard) material and associated interface are modeled in a Lagrangian fashion. Loads are transferred between the hard and soft materials via explicit transient dynamics contact algorithms. The use of these contact algorithms remove the requirement of node-tonode matching at the soft-hard interface. In the context of the operator-split ALE algorithm, a single Lagrangian step is performed using a mesh to mesh contact algorithm. At the end of the Lagrangian step the meshes will be slightly offset at the interface but non-interpenetrating. The ALE mesh nodes at the interface are then remeshed to their initial location relative to the Lagrangian body faces and the ALE mesh is smoothed, translated and rotated to follow Lagrangian body. Robust remeshing in the ALE region is required for success of this algorithm, and we describe current work in this area. The second method is an overlapping grid methodology that requires mapping of information between a Lagrangian mesh and an ALE mesh. The Lagrangian mesh describes a relatively hard body that interacts with softer material contained in the ALE mesh. A predicted solution for the velocity field is performed independently on both meshes. Element-centered velocity and momentum are transferred between the meshes using the volume transfer capability implemented in contact algorithms. Data from the ALE mesh is mapped to a phantom mesh that surrounds the Lagrangian mesh, providing for the reaction to the predicted motion of the Lagrangian material. Data from the Lagrangian mesh is mapped directly to the ALE mesh. A momentum balance is performed on both meshes to adjust the velocity field to account for the interaction of the material from the other mesh. Subsequent, remeshing and remapping of the ALE mesh is performed to allow large deformation of the softer material. We overview current progress using this approach and discuss avenues for future research and development.

Wong, Michael K. W.; Voth, Thomas Eugene; Hensinger, David M.; Bishop, Joseph E.; Robinson, Allen Conrad

2005-06-01

436

Topological BF field theory description of topological insulators

Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.

Cho, Gil Young [Department of Physics, University of California, Berkeley, CA 94720 (United States); Moore, Joel E., E-mail: jemoore@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)

2011-06-15

437

A theory is developed to describe quantitatively the idea that in an ionized gas subject to an imposed magnetic field, such as the ionosphere, the lines of magnetic flux are approximately equipotential lines. The ionosphere is assumed to be horizontally stratified, and the case in which the earth's magnetic field is vertical is considered. Small-scale electro- static fields are studied

1959-01-01

438

Two Problems in the Galois Theory of Differential Fields for the Field of Formal Power Series

NASA Astrophysics Data System (ADS)

The direct problem in the Galois theory of differential fields for a homogeneous linear differential equation of the second order over the field C((x)) is solved, and a classification of SL(2)-extensions and a description of the Picard-Vessiot extensions of this field are given.Bibliography: 5 titles.

Grigorenko, N. V.

1980-04-01

439

Competitive adsorption of counterions of multiple species to charged surfaces is studied by a size-effect-included mean-field theory and Monte Carlo (MC) simulations. The mean-field electrostatic free-energy functional of ionic concentrations, constrained by Poisson's equation, is numerically minimized by an augmented Lagrangian multiplier method. Unrestricted primitive models and canonical ensemble MC simulations with the Metropolis criterion are used to predict the ionic distributions around a charged surface. It is found that, for a low surface charge density, the adsorption of ions with a higher valence is preferable, agreeing with existing studies. For a highly charged surface, both the mean-field theory and the MC simulations demonstrate that the counterions bind tightly around the charged surface, resulting in a stratification of counterions of different species. The competition between mixed entropy and electrostatic energetics leads to a compromise that the ionic species with a higher valence-to-volume ratio has a larger probability to form the first layer of stratification. In particular, the MC simulations confirm the crucial role of ionic valence-to-volume ratios in the competitive adsorption to charged surfaces that had been previously predicted by the mean-field theory. The charge inversion for ionic systems with salt is predicted by the MC simulations but not by the mean-field theory. This work provides a better understanding of competitive adsorption of counterions to charged surfaces and calls for further studies on the ionic size effect with application to large-scale biomolecular modeling. PMID:22680474

Wen, Jiayi; Zhou, Shenggao; Xu, Zhenli; Li, Bo

2012-04-01

440

NASA Technical Reports Server (NTRS)

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.

Liou, Meng-Sing

1993-01-01

441

Fast computation of Lagrangian coherent structures: algorithms and error analysis

NASA Astrophysics Data System (ADS)

This work investigates a number of efficient methods for computing finite time Lyapunov exponent (FTLE) fields in unsteady flows by approximating the particle flow map and eliminating redundant particle integrations in neighboring flow maps. Ridges of the FTLE fields are Lagrangian coherent structures (LCS) and provide an unsteady analogue of invariant manifolds from dynamical systems theory. The fast methods fall into two categories, unidirectional and bidirectional, depending on whether flow maps in one or both time directions are composed to form an approximate flow map. An error analysis is presented which shows that the unidirectional methods are accurate while the bidirectional methods have significant error which is aligned with the opposite time coherent structures. This relies on the fact that material from the positive time LCS attracts onto the negative time LCS near time-dependent saddle points.

Brunton, Steven; Rowley, Clarence

2009-11-01

442

Vacuum Stability of the Wrong Sign (-? 6) Scalar Field Theory

NASA Astrophysics Data System (ADS)

We apply the effective potential method to study the vacuum stability of the bounded from above (-? 6) (unstable) quantum field potential. The stability (?E/?b = 0) and the mass renormalization (? 2 E/?b 2 = M 2) conditions force the effective potential of this theory to be bounded from below (stable). Since bounded from below potentials are always associated with localized wave functions, the algorithm we use replaces the boundary condition applied to the wave functions in the complex contour method by two stability conditions on the effective potential obtained. To test the validity of our calculations, we show that our variational predictions can reproduce exactly the results in the literature for the {PT}-symmetric ? 4 theory. We then extend the applications of the algorithm to the unstudied stability problem of the bounded from above (-? 6) scalar field theory where classical analysis prohibits the existence of a stable spectrum. Concerning this, we calculated the effective potential up to first order in the couplings in d space-time dimensions. We find that a Hermitian effective theory is instable while a non-Hermitian but {PT}-symmetric effective theory characterized by a pure imaginary vacuum condensate is stable (bounded from below) which is against the classical predictions of the instability of the theory. We assert that the work presented here represents the first calculations that advocates the stability of the (-? 6) scalar potential.

Shalaby, Abouzeid M.

2014-05-01

443

Fluctuations in ``Brown-Rho scaled'' chiral Lagrangians

NASA Astrophysics Data System (ADS)

We develop arguments for ``mapping'' the effective chiral Lagrangian whose parameters are given by ``Brown-Rho'' (BR) scaling to a Landau Fermi-liquid fixed-point theory for nuclear matter in describing fluctuations in various flavor (e.g., strangeness) directions. We use for this purpose the effective Lagrangian used by Furnstahl, Tang, and Serot that incorporates the trace anomaly of QCD in terms of a light-quark (quarkonium) degree of freedom with the heavy (gluonium) degree of freedom integrated out. The large anomalous dimension dan~5/3 for the scalar field found by Furnstahl et al. to be needed for a correct description of nuclear matter is interpreted as an indication for a strong-coupling regime and the ground state given by the BR-scaled parameters is suggested as the background around which fluctuations can be rendered weak so that mean-field approximation is reliable. We construct a simple model with BR-scaled parameters that provides a satisfactory description of the properties of matter at normal nuclear matter density. Given this, fluctuations around the BR-scaled background are dominated by tree diagrams. Our reasoning relies heavily on recent developments in the study of nucleon and kaon properties in normal and dense nuclear matter, e.g., nucleon and kaon flows in heavy-ion processes, kaonic atoms, and kaon condensation in dense compact-star matter.

Song, Chaejun; Brown, G. E.; Min, Dong-Pil; Rho, Mannque

1997-10-01

444

On a solitonic approach to coloured reggeon field theory

Summary The intrinsic parallelism in the physical contents of the nonlinear Schrödinger equation (NLSE) and the nonrelativistic reggeon\\u000a field theory (RFT) has been utilised to apply the nonperturbative approach to RFT. Against the usual field-theoretic approach,\\u000a the path integral method has been utilized to achieve semi-classical quantization of the solitonic mode extracted by the inverse\\u000a scattering transform. The eigenfrequencies and the

A. Roy Chowdhury; B. Sidhanta

1986-01-01

445

Emergent matter from 3D generalized group field theories

NASA Astrophysics Data System (ADS)

We identify classical solutions of a generalized group field theory (GFT) model in three dimensions and study the corresponding perturbations, deriving their effective dynamics. We discuss their interpretation as emergent matter fields. This allows us on the one hand to test the proposed mechanism for emergence of matter as a phase of GFT, and on the other hand to expose some limitations of the generalized GFT formalism.

Di Mare, Alessandro; Oriti, Daniele

2010-07-01

446

New physical Lagrangian tracer

A physical Lagrangian tracer will be operational and available for use within the near future. The tracer is an adjustable buoyancy constant volume balloon with an onboard microprocessor to serve an appropriate array of sensors, and to control buoyancy. Tracking and data reporting is to be accomplished via the ARGOS satellite-borne data system, yielding both a local and a world-wide capability. 5 references, 1 figure.

Zak, B.D.

1984-01-01

447

Gravity, Time, and Lagrangians

ERIC Educational Resources Information Center

Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…

Huggins, Elisha

2010-01-01

448

Non-perturbative aspects of supersymmetric field theories and string theory

NASA Astrophysics Data System (ADS)

Non-perturbative effects play an important role both in field theory and in string theory. They are, however, difficult to access. Four aspects of such effects are considered in this dissertation. The first topic is stringy cosmology. By trying to examine a cosmological scenario that is based on generic features of string theories, we learn about possible new cosmological scenarios and on qualitative features that are required from non-perturbative dynamics in string theory. The second topic in duality in N=1 gauge theory. The results present include a relatively general method for generating duals to given gauge theories, some specific examples and new algebraic classes of operators in superconformal fixed points. The third topic is duality in string theory. The results focus on some aspects of D- branes in string duality, and also include a new anomaly cancelation mechanism in six dimensions. The fourth topic is matrix theory, which is a recent proposal for the non- perturbative definition of eleven dimensional supergravity and its stringy descendants. Among the results presented is a new definition of Matrix theory in terms of superconformal fixed point in six dimensions, and its implications for our understanding of space-time.

Berkooz, Micha

449

NASA Technical Reports Server (NTRS)

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Liou, Meng-Sing

1995-01-01

450

We discuss the breakdown of the perturbative unitarity of noncommutative quantum field theories in an electric-type background in the light of string theory. We consider the analytic structure of string loop two-point functions using a suitable off-shell continuation, and then study the zero slope limit of Seiberg and Witten. In this way we pick up how the unphysical tachyonic branch

Alessandro Torrielli; G. Galilei

2003-01-01

451

Geometry of Hamiltonian n-vector fields in multisymplectic field theory

Multisymplectic geometry—which originates from the well known De Donder–Weyl (DW) theory—is a natural framework for the study of classical field theories. Recently, two algebraic structures have been put forward to encode a given theory algebraically. Those structures are formulated on finite dimensional spaces, which seems to be surprising at first.In this paper, we investigate the correspondence of Hamiltonian functions and

Cornelius Paufler; Hartmann Römer

2002-01-01

452

The Effective Field Theory Approach to Fluid Dynamics

NASA Astrophysics Data System (ADS)

In this thesis we initiate a systematic study of fluid dynamics using the effective field theory (EFT) program. We consider the canonical quantization of an ordinary fluid in an attempt to discover if there is some kind of quantum mechanical inconsistency with ordinary fluids at zero temperature. The system exhibits a number of peculiarities associated with the vortex degrees of freedom. We also study the dynamics of a nearly incompressible fluid via (classical) effective field theory. In the kinematical regime corresponding to near incompressibility (small fluid velocities and accelerations), compressional modes are, by definition, difficult to excite, and can be dealt with perturbatively. We systematically outline the corresponding perturbative expansion, which can be thought of as an expansion in the ratio of fluid velocity and speed of sound. This perturbation theory allows us to compute many interesting quantities associated with sound-flow interactions. Additionally, we also improve on the so-called vortex filament model, by providing a local field theory describing the dynamics of vortex-line systems and their interaction with sound, to all orders in perturbation theory. Next, we develop a cosmological model where primordial inflation is driven by a 'solid'. The low energy EFT describing such a system is just a less symmetric version of the action of a fluid---it lacks the volume preserving diffeomorphism. The symmetry breaking pattern of this system differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations. And finally, we introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory to a generic sector that "lives in the fluid'', which corresponds physically to the microscopic constituents of the fluid. At linear order in perturbations, the symmetries, the derivative expansion, and the assumption that this microscopic sector is thermalized, allow us to characterize the leading dissipative effects at low frequencies via three parameters only, which correspond to bulk viscosity, shear viscosity, and---in the presence of a conserved charge---heat conduction. Using our methods we re-derive the Kubo relations for these transport coefficients.

Endlich, Solomon George Shamsuddin Osman

453

Effective Lagrangians in Elementary Particle Physics

Non-linear effective Lagrangians are constructed to represent the low energy phenomenology of elementary particles. As approximate descriptions of the dynamics of hadrons, these models simulate the expected {but unproven} behavior of more complex theories such as quantum Chromo-dynamics {QCD}. A general formalism for non-linear models was developed in the late 1960's by Coleman, Wess and Zumino. This dissertation utilizes and

Charles Garrett Trahern

1982-01-01

454

Theory of a ring laser. [electromagnetic field and wave equations

NASA Technical Reports Server (NTRS)

Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.

Menegozzi, L. N.; Lamb, W. E., Jr.

1973-01-01

455

Higher-dimensional Algebra and Topological Quantum Field Theory

The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and outline a program in which n-dimensional TQFTs are to be described as n-category representations. First we describe a \\

John C. Baez; James Dolan

1995-01-01

456

Gauge symmetries in (super)string field theory

We study gauge symmetries of the cubic formulation of open-string field theory in light of the recently discovered associativity anomalies. It is shown that the gauge group includes arbitrary general coordinate transformations, in accord with the existence of closed-string configurations. In the case of the superstring, supersymmetry is shown to be a gauge symmetry.

Zongan Qiu; Andrew Strominger

1987-01-01

457

Operator formulation of interacting string field theory (I)

We present an explicit, operator construction of Witten's interacting string field theory. The approach is based on a Fock space representation of string functionals and delta-function overlaps. The construction is achieved by employing conformal mapping and Neumann function techniques. The gauge invariant interaction vertex is constructed; on physical states it is shown to lead to correct dual model amplitudes. The

David J. Gross; Antal Jevicki

1987-01-01

458