Symmetries in Lagrangian Field Theory
NASA Astrophysics Data System (ADS)
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1? of a fiber bundle ? : E ? ?k where ?k is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
Theory of Classical Higgs Fields. II. Lagrangians
G. Sardanashvily; A. Kurov
2014-11-27
We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $P\\to X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/H\\to X$ are treated as classical Higgs fields. In this theory, matter fields with an exact symmetry group $H$ are described by sections of a composite bundle $Y\\to P/H\\to X$. We show that their gauge $G$-invariant Lagrangian necessarily factorizes through a vertical covariant differential on $Y$ defined by a principal connection on an $H$-principal bundle $P\\to P/H$.
Lagrangian-Hamiltonian unified formalism for field theory
A. Echeverría-Enríquez; C. López; J. Marín-Solano; M. C. Muñoz-Lecanda; N. Román-Roy
2004-02-13
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for PDE's.
LAGRANGIAN-HAMILTONIAN UNIFIED FORMALISM FOR FIELD THEORY
Arturo Echeverr ´ õa-Enr ´ õquez; Carlos L ´; Miguel C. Mu; Narciso Roman-Roy
The Rusk-Skinner formalism was developed in order to give a geometrical unified formal- ism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this
Lagrangian-Hamiltonian unified formalism for field theory
Arturo Echeverría-Enríquez; Jesús Marín-Solano; Miguel C. Muñoz-Lecanda; Narciso Román-Roy
2004-01-01
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description
Conditions for the existence of a Lagrangian in field theory
Farias, J.R.
1982-12-15
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.
Unified Theory of Field with Modul of Squared Curvature as Lagrangian
V. I. Drosdov
2001-04-27
The 4-D theory with connection components Gamma^k_{mn} as field variables and module of squared curvature |R^k_{lmn}R^{lmn}_k| as Lagrangian is described. The Maxwell equations, the Lorentz condition and the gravity field equation, that agrees with Newton's theory, result from equations of motion.
A study on relativistic lagrangian field theories with non-topological soliton solutions
Diaz-Alonso, J. [LUTH, Observatoire de Paris, CNRS, Universite Paris Diderot, 5 Place Jules Janssen, 92190 Meudon (France); Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias (Spain)], E-mail: joaquin.diaz@obspm.fr; Rubiera-Garcia, D. [Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias (Spain)
2009-04-15
We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call 'admissible' models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite-energy electrostatic spherically symmetric solutions which, unlike the (multi-) scalar case, are not always stable. The variational analysis of the energy functional leads now to supplementary restrictions to be imposed on the lagrangian densities in order to ensure the linear stability of the solitons. We establish a correspondence between any admissible soliton-supporting (multi-) scalar model and a family of admissible generalized gauge models supporting finite-energy electrostatic point-like solutions. Conversely, for each admissible soliton-supporting gauge-invariant model there is an associated unique admissible (multi-) scalar model with soliton solutions. This shows the exhaustive character of the admissibility and stability conditions in determining the class of soliton-supporting generalized gauge models. The usual Born-Infeld electrodynamic theory and its non-abelian extensions are shown to be (very particular) examples of one of these families.
NASA Technical Reports Server (NTRS)
Guertin, R. F.; Wilson, T. L.
1977-01-01
To illustrate that a relativistic field theory need not be manifestly covariant, Lorentz-invariant Lagrangian densities are constructed that yield the equation satisfied by an interacting (two-component) Sakata-Taketani spin-0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric second-rank tensor, and a symmetric second-rank tensor, with the results specialized to electromagnetic interactions. For either of the two second-rank couplings, the equation is found to describe noncausal wave propagation, a property that is apparent from the dependence of the coefficients of the space derivatives on the external field; in contrast, the noncausality of the corresponding manifestly covariant Duffin-Kemmer-Petiau spin-0 equation is not so obvious. The possibilities for generalizing the results to higher spin theories involving only the essential 2(2J + 1) components for a particle with a definite spin J and mass m are discussed in considerable detail.
The Lagrangian-space Effective Field Theory of large scale structures
NASA Astrophysics Data System (ADS)
Porto, Rafael A.; Senatore, Leonardo; Zaldarriaga, Matias
2014-05-01
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.
Emmanuele Battista; Simone Dell'Agnello; Giampiero Esposito; Luciano Di Fiore; Jules Simo; Aniello Grado
2015-07-10
In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. We then evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. By virtue of the effective-gravity correction to the longdistance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. Thus, it is possible to conceive a new, first-generation laser ranging test of general relativity with a relative accuracy in between 1/100 and 1/1000, by measuring the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. This will be the basis to consider a second-generation experiment to set experimental constraints on deviations of effective field theories of gravity from general relativity.
P- and T-Violating Lagrangians in Chiral Effective Field Theory and Nuclear Electric Dipole Moments
J. Bsaisou; Ulf-G. Meißner; A. Nogga; A. Wirzba
2015-04-30
A scheme to derive hadronic interactions induced by effective multi-quark terms is presented within the framework of chiral effective field theory. It is employed to work out the list of parity- and time-reversal-symmetry-violating hadronic interactions that are relevant for the computation of nuclear contributions to the electric dipole moments of the hydrogen-2, helium-3 and hydrogen-3 nuclei. We also derive the scattering and Faddeev equations required to compute electromagnetic form factors in general and electric dipole moments in particular.
Battista, Emmanuele; Esposito, Giampiero; Di Fiore, Luciano; Simo, Jules; Grado, Aniello
2015-01-01
In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. We then evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. By virtue of the effective-gravity correction to the longdistance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for ...
Hamiltonian quantization of effective Lagrangians with massive vector fields
Carsten Grosse-Knetter
1993-01-01
Effective Lagrangians containing arbitrary interactions of massive vector fields are quantized within the Hamiltonian path-integral formalism. It is proven that the correct Hamiltonian quantization of these models yields the same result as naive Lagrangian quantization (Matthew's theorem). This theorem holds for models without gauge freedom as well as for (linearly or nonlinearly realized) spontaneously broken gauge theories. The Stueckelberg formalism,
Thermal Effective Lagrangian of Static Gravitational Fields
F T Brandt; J B Siqueira
2012-03-08
We compute the effective Lagrangian of static gravitational fields interacting with thermal fields. Our approach employs the usual imaginary time formalism as well as the equivalence between the static and space-time independent external gravitational fields. This allows to obtain a closed form expression for the thermal effective Lagrangian in $d$ space-time dimensions.
Covariant Noncommutative Field Theory
Estrada-Jimenez, S. [Licenciaturas en Fisica y en Matematicas, Facultad de Ingenieria, Universidad Autonoma de Chiapas Calle 4a Ote. Nte. 1428, Tuxtla Gutierrez, Chiapas (Mexico); Garcia-Compean, H. [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN P.O. Box 14-740, 07000 Mexico D.F., Mexico and Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey Via del Conocimiento 201, Parque de Investigacion e Innovacion Tecnologica (PIIT) Autopista nueva al Aeropuerto km 9.5, Lote 1, Manzana 29, cp. 66600 Apodaca Nuevo Leon (Mexico); Obregon, O. [Instituto de Fisica de la Universidad de Guanajuato P.O. Box E-143, 37150 Leon Gto. (Mexico); Ramirez, C. [Facultad de Ciencias Fisico Matematicas, Universidad Autonoma de Puebla, P.O. Box 1364, 72000 Puebla (Mexico)
2008-07-02
The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.
Convolution Lagrangian perturbation theory for biased tracers
NASA Astrophysics Data System (ADS)
Carlson, Jordan; Reid, Beth; White, Martin
2013-02-01
We present a new formulation of Lagrangian perturbation theory which allows accurate predictions of the real- and redshift-space correlation functions of the mass field and dark matter haloes. Our formulation involves a non-perturbative resummation of Lagrangian perturbation theory and indeed can be viewed as a partial resummation of the formalism of Matsubara in which we keep exponentiated all of the terms which tend to a constant at large separation. One of the key features of our method is that we naturally recover the Zel'dovich approximation as the lowest order of our expansion for the matter correlation function. We compare our results against a suite of N-body simulations and obtain good agreement for the correlation functions in real space and for the monopole correlation function in redshift space. The agreement becomes worse for higher multipole moments of the redshift-space, halo correlation function. Our formalism naturally includes non-linear bias and explains the strong bias-dependence of the multipole moments of the redshift-space correlation function seen in N-body simulations.
NASA Astrophysics Data System (ADS)
Minazzoli, Olivier; Hees, Aurélien
2013-08-01
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.
Olivier Minazzoli; Aurélien Hees
2013-08-13
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.
LE JOURNAL DE PHYSIQUE THE LAGRANGIAN THEORY OF POLYMER SOLUTIONS
Boyer, Edmond
LE JOURNAL DE PHYSIQUE THE LAGRANGIAN THEORY OF POLYMER SOLUTIONS AT INTERMEDIATE CONCENTRATIONS J'expérience. Abstract. 2014 De Gennes has shown that the properties of an isolated polymer in a solution (a chain in the absence of an external field. This result in generalized to the case of polymer solutions at intermediate
Relativistic Lagrangian displacement field and tensor perturbations
Cornelius Rampf; Alexander Wiegand
2014-12-14
We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the Lagrangian frame. These techniques are (a) from defining a local set of Eulerian coordinates embedded into the Lagrangian frame; (b) from performing a specific gauge transformation; and (c) from a fully non-perturbative approach based on the ADM split. The latter approach shows that this decomposition is not tied to a specific perturbative formulation for the solution of the Einstein equations. Rather, it can be defined at the level of the non-perturbative coordinate change from the Lagrangian to the Eulerian description. Studying such different techniques is useful because it allows us to compare and develop further the various approximation techniques available in the Lagrangian formulation. We find that one has to solve the gravitational wave equation in the relativistic analysis, otherwise the corresponding Newtonian limit will necessarily contain spurious non-propagating tensor artefacts at second order in the Eulerian frame. We also derive the magnetic part of the Weyl tensor in the Lagrangian frame, and find that it is not only excited by gravitational waves but also by tensor perturbations which are induced through the non-linear frame-dragging. We apply our findings to calculate for the first time the relativistic displacement field, up to second order, for a $\\Lambda$CDM Universe in the presence of a local primordial non-Gaussian component. Finally, we also comment on recent claims about whether mass conservation in the Lagrangian frame is violated.
Lagrangian formulation of neoclassical transport theory
Bernstein, I.B.; Molvig, K.
1983-06-01
Neoclassical transport theory is developed in a Lagrangian formulation in contrast to the usual Eulerian development. The Lagrangian formulation is constructed from the three actions: magnetic moment, parallel invariant, and bounce-averaged poloidal flux. By averaging over the fast orbital time scales, an equation in the actions alone of the Fokker--Planck type is obtained. The coefficients give the rates of the elementary neoclassical scattering processes. This action space form of the kinetic equation contains in explicit form processes like banana diffusion and the kinematic Ware pinch. The associated fluxes can be computed by simple moments without having deviations from the local Maxwellian. All the trapped-particle contributions are of this explicit type. Another class of fluxes arise from perturbations to the Maxwellian and are termed implicit. The decomposition of the fluxes into explicit and implicit parts is a key feature of the Lagrangian formulation. These contributions correspond to distinct physical processes and have separate Onsager symmetry theorems (explicit and implicit) for their respective transport matrices. The theory does not depend on the details of the Fokker--Planck coefficients but only on some very general properties and is thus applicable: without modification of the formalism: to nonaxisymmetric and turbulent systems. This general formulation is the primary purpose of the work. To benchmark the theory, in the present paper, the tokamak transport coefficients (for the Lorentz gas) are computed and compared to the known Eulerian results, demonstrating the equivalence of the two formulations. The elementary processes responsible for the neoclassical pinch and bootstrap effects (somewhat obscured in the Eulerian picture) are identified and the physical basis for their Onsager symmetry relationship is clarified.
Using Lagrangian perturbation theory for precision cosmology
Sugiyama, Naonori S., E-mail: nao.s.sugiyama@gmail.com [Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544-1001 (United States); Astronomical Institute, Tohoku University, 6-3, Aramakijiaoba, Sendai 980-8578 (Japan)
2014-06-10
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{sup –1} and z = 0.35 to better than 2%.
Using Lagrangian Perturbation Theory for Precision Cosmology
NASA Astrophysics Data System (ADS)
Sugiyama, Naonori S.
2014-06-01
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%.
Vacuum birefringence from the effective Lagrangian of the electromagnetic field
Kruglov, S. I. [University of Toronto at Scarborough, Physical and Environmental Sciences Department, 1265 Military Trail, Toronto, Ontario, M1C 1A4 (Canada)
2007-06-01
The propagation of a linearly polarized laser beam in the external transverse magnetic field is studied. We explore the effective Lagrangian of the electromagnetic field. With the help of the effective Lagrangian, Stokes parameters, induced ellipticity, and the angular rotation of the polarization plane of the beam are evaluated. Ellipticity measured in the PVLAS experiment allows us to obtain the relation between two parameters in the effective Lagrangian.
String perturbation theory and effective Lagrangians
Klebanov, I.
1987-09-01
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.
Topics in low-dimensional field theory
Crescimanno, M.J.
1991-04-30
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.
Particle transport in a random velocity field with Lagrangian statistics.
Olla, Piero
2002-11-01
The transport properties of a random velocity field with Kolmogorov spectrum and time correlations defined along Lagrangian trajectories are analyzed. The analysis is carried out in the limit of short correlation times, as a perturbation theory in the ratio, scale by scale, of the eddy decay and turnover time. Various quantities such as the Batchelor constant and the dimensionless constants entering the expression for particle relative and self-diffusion are given in terms of this ratio and of the Kolmogorov constant. Particular attention is paid to particles with finite inertia. The self-diffusion properties of a particle with Stokes time longer than the Kolmogorov time are determined, verifying on an analytical example the dimensional results of Olla [Phys. Fluids 14, 4266 (2002)]. Expressions for the fluid velocity Lagrangian correlations and correlation times along a solid particle trajectory are provided in several parameter regimes, including the infinite Stokes time limit corresponding to Eulerian correlations. The concentration fluctuation spectrum and the nonergodic properties of a suspension of heavy particles in a turbulent flow, in the same regime, are analyzed. The concentration spectrum is predicted to obey, above the scale of eddies with lifetime equal to the Stokes time, a power law with universal -4/3 exponent, and to be otherwise independent of the nature of the turbulent flow. A preference of the solid particle to lie in less energetic regions of the flow is observed. PMID:12513593
Integrable Field Theories with Defects
J. F. Gomes; L. H. Ymai; A. H. Zimerman
2006-09-13
The structure of integrable field theories in the presence of defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the super sinh-Gordon model is constructed and shown to generate the Backlund transformations for its soliton solutions.
The soft supersymmetry-breaking Lagrangian: theory and applications
D. J. H. Chung; L. L. Everett; G. L. Kane; S. F. King; J. Lykken; Lian-Tao Wang
2005-01-01
After an introduction recalling the theoretical motivation for low energy (100GeV to TeV scale) supersymmetry, this review describes the theory and experimental implications of the soft supersymmetry-breaking Lagrangian of the general minimal supersymmetric standard model (MSSM). Extensions to include neutrino masses and nonminimal theories are also discussed. Topics covered include models of supersymmetry breaking, phenomenological constraints from electroweak symmetry breaking,
Cosmological structure formation with augmented Lagrangian perturbation theory
NASA Astrophysics Data System (ADS)
Kitaura, Francisco-Shu; Heß, Steffen
2013-08-01
We present a new fast and efficient approach to model structure formation with augmented Lagrangian perturbation theory (ALPT). Our method is based on splitting the displacement field into a long- and a short-range component. The long-range component is computed by second-order LPT (2LPT). This approximation contains a tidal non-local and non-linear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low-density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zel'dovich approximation). We propose to combine both approximations using for the short-range displacement field the SC solution. A Gaussian filter with a smoothing radius rS is used to separate between both regimes. We use the result of 25 dark-matter-only N-body simulations to benchmark at z = 0 the different approximations: first-, second-, third-order LPT, SC and our novel combined ALPT model. This comparison demonstrates that our method improves previous approximations at all scales showing ˜25 and ˜75 per cent higher correlation than 2LPT with the N-body solution at k = 1 and 2 h Mpc-1, respectively. We conduct a parameter study to determine the optimal range of smoothing radii and find that the maximum correlation is achieved with rS = 4-5 h-1 Mpc. This structure formation approach could be used for various purposes, such as setting-up initial conditions for N-body simulations, generating mock galaxy catalogues, cosmic web analysis or for reconstructions of the primordial density fluctuations.
Costa-Quintana, J., E-mail: joan.costa@uab.cat; Lopez-Aguilar, F., E-mail: fernando.lopez@uab.cat
2012-08-15
We analyze the conditions of the electromagnetic potentials for systems with electric and magnetic charges and the Lagrangian theory with these potentials. The constructed Lagrangian function is valid for obtaining the field equations and the extended Lorentz force for dyonic charges for both relativistic particles in vacuum and non-relativistic entities in solids. In a second part, with the one-body Hamiltonian of independent particles in external fields, we explore some dual properties of the dyonic system under external fields. We analyze the possible diamagnetic (and 'diaelectric') response of magnetic monopoles under a weak and constant electromagnetic field and the theory of Landau levels in the case of magnetic charges under strong electromagnetic constant fields. - Highlights: Black-Right-Pointing-Pointer We study the Lagrangian formalism for magnetic charges. Black-Right-Pointing-Pointer We analyze the electromagnetic potentials for dyons. Black-Right-Pointing-Pointer We study two dual properties of solid systems with magnetic charges. Black-Right-Pointing-Pointer A quantum study of solids with monopoles under electromagnetic constant fields.
Regular hyperbolicity, dominant energy condition and causality for Lagrangian theory of maps
Willie Wai-Yeung Wong
2011-05-16
The goal of the present paper is three-fold. First is to clarify the connection between the dominant energy condition and hyperbolicity properties of Lagrangian field theories. Second is to provide further analysis on the breakdown of hyperbolicity for the Skyrme model, sharpening the results of Crutchfield and Bell and comparing against a result of Gibbons, and provide a local well-posedness result for the dynamical problem in the Skyrme model. Third is to provide a short summary of the framework of regular hyperbolicity of Christodoulou for the relativity community. In the process, a general theorem about dominant energy conditions for Lagrangian theories of maps is proved, as well as several results concerning hyperbolicity of those maps.
Axiomatic classical (prequantum) field theory. Jet formalism
G. Sardanashvily
2006-01-01
In contrast with QFT, classical field theory can be formulated in a strict mathematical way if one defines even classical fields as sections of smooth fiber bundles. Formalism of jet manifolds provides the conventional language of dynamic systems (nonlinear differential equations and operators) on fiber bundles. Lagrangian theory on fiber bundles is algebraically formulated in terms of the variational bicomplex
Quantum noncanonical field theory: Symmetries and interaction
Carmona, J. M.; Cortes, J. L.; Indurain, J.; Mazon, D. [Departamento de Fisica Teorica, Universidad de Zaragoza, Zaragoza 50009 (Spain)
2009-11-15
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincare invariance in an auxiliary spacetime is found in the Lagrangian version of the path integral formulation. This invariance is contrasted with the idea of doubly (or deformed) special relativity. This analysis is then used to go from the free theory of a complex field to an interacting field theory.
Propagating modes in gauge field theories of gravity
R. Kuhfuss; J. Nitsch
1986-01-01
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.
Field equations and conservation laws in the nonsymmetric gravitational theory
J. Légaré; J. W. Moffat
1995-01-01
The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived. Among these are the generalized Bianchi identities and the law of energy-momentum conservation. The Lagrangian density is expanded to second-order, and treated as an “Einstein plus fields”
Variational Principles for multisymplectic second-order classical field theories
Pedro Daniel Prieto-Martínez; Narciso Román-Roy
2015-03-31
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.
Transients from initial conditions based on Lagrangian perturbation theory in N-body simulations
Takayuki Tatekawa; Shuntaro Mizuno
2007-11-28
We explore the initial conditions for cosmological N-body simulations suitable for calculating the skewness and kurtosis of the density field. In general, the initial conditions based on the perturbation theory (PT) provide incorrect second-order and higher-order growth. These errors implied by the use of the perturbation theory to set up the initial conditions in N-body simulations are called transients. Unless these transients are completely suppressed compared with the dominant growing mode, we can not reproduce the correct evolution of cumulants with orders higher than two, even though there is no problem with the numerical scheme. We investigate the impact of transients on the observable statistical quantities by performing $N$-body simulations with initial conditions based on Lagrangian perturbation theory (LPT). We show that the effects of transients on the kurtosis from the initial conditions, based on second-order Lagrangian perturbation theory (2LPT) have almost disappeared by $z\\sim5$, as long as the initial conditions are set at $z > 30$. This means that for practical purposes, the initial conditions based on 2LPT are accurate enough for numerical calculations of skewness and kurtosis.
Adler-Kostant-Symes systems as Lagrangian gauge theories
L. Feher; A. Gabor
2002-02-22
It is well known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This is achieved by constructing a Lagrangian with gauge symmetry in such a way that, by means of the Dirac algorithm, this Lagrangian reproduces the Adler-Kostant-Symes system whose Hamiltonian is the quadratic form associated with the scalar product on the Lie algebra.
About non standard Lagrangians in cosmology
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
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.
NASA Astrophysics Data System (ADS)
Buchbinder, I. L.; Krykhtin, V. A.; Tsulaia, M.
2015-07-01
We consider massive half-integer higher spin fields coupled to an external constant electromagnetic field in flat space of an arbitrary dimension and construct a gauge invariant Lagrangian in the linear approximation in the external field. A procedure for finding the gauge-invariant Lagrangians is based on the BRST construction where no off-shell constraints on the fields and on the gauge parameters are imposed from the very beginning. As an example of the general procedure, we derive a gauge invariant Lagrangian for a massive fermionic field with spin 3/2 which contains a set of auxiliary fields and gauge symmetries.
Cosmological status of Lagrangian theory of density perturbations
V. Strokov
2006-12-14
We show that hydrodynamical and field approaches in theory of cosmological scalar perturbations are equivalent for a single medium. We also give relations between notations introduced by V. Lukash, J. Bardeen, J. Bardeen et al. and G. Chibisov and V. Mukhanov.
Francesco Guerra
2005-10-26
A coincise review about Euclidean (Quantum) Field Theory is presented. It deals with the general structural properties, the connections with Quantum Field Theory, the exploitation in Constructive Quantum Field Theory, and the physical interpretation.
NASA Astrophysics Data System (ADS)
Buchbinder, I. L.; Reshetnyak, A.
2012-09-01
We construct a Lagrangian description of irreducible integer higher spin representations of the Poincaré-group with an arbitrary Young tableaux having k rows, on a basis of the universal BRST approach. Starting with a description of bosonic mixed-symmetry higher spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with special Poincaré module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincaré-group representations) into a first-class constraint system. For this purpose, we find, for the first time, auxiliary representations of the constraint subalgebra, to be isomorphic due to Howe duality to sp(2k) algebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We propose a universal procedure of constructing unconstrained gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive bosonic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincaré-group representation. As examples of the general procedure, we formulate the method of Lagrangian construction for bosonic fields subject to arbitrary Young tableaux having 3 rows and derive the gauge-invariant Lagrangian for new model of massless rank-4 tensor field with spin (2,1,1) and second stage reducible gauge symmetries.
Hart, Gus
Electromagnetic Field Theory BO THIDÉ UPSILON BOOKS #12;#12;ELECTROMAGNETIC FIELD THEORY #12;#12;Electromagnetic Field Theory BO THIDÉ Swedish Institute of Space Physics and Department of Astronomy and Space, Sweden UPSILON BOOKS · COMMUNA AB · UPPSALA · SWEDEN #12;Also available ELECTROMAGNETIC FIELD THEORY
Effective Lagrangian at Cubic Order in Electromagnetic Fields and Vacuum Birefringence
S. I. Kruglov
2007-08-09
The effective Lagrangian of electromagnetic fields at the cubic order in field strength has been considered. This generalized Lagrangian is motivated by electrodynamics on non-commutative spaces. We find the canonical and symmetrical energy-momentum tensors and show that they possess non-zero traces. The propagation of a linearly polarized laser beam in the external transverse magnetic field is investigated. We evaluate the induced ellipticity which allows us to obtain a constraint on parameters introduced from the PVLAS experimental data.
Washington Taylor
2006-06-28
This elementary introduction to string field theory highlights the features and the limitations of this approach to quantum gravity as it is currently understood. String field theory is a formulation of string theory as a field theory in space-time with an infinite number of massive fields. Although existing constructions of string field theory require expanding around a fixed choice of space-time background, the theory is in principle background-independent, in the sense that different backgrounds can be realized as different field configurations in the theory. String field theory is the only string formalism developed so far which, in principle, has the potential to systematically address questions involving multiple asymptotically distinct string backgrounds. Thus, although it is not yet well defined as a quantum theory, string field theory may eventually be helpful for understanding questions related to cosmology in string theory.
NASA Astrophysics Data System (ADS)
Reshetnyak, A.
2013-04-01
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
Euler-Poincare reduction for discrete field theories
Vankerschaver, Joris [Department of Mathematical Physics and Astronomy, University of Ghent, Krijgslaan 281, B-9000 Ghent (Belgium)
2007-03-15
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed.
On background-independent open-string field theory
Edward Witten
1992-01-01
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
On exact tachyon potential in open string field theory
Anton A. Gerasimov; Samson L. Shatashvili
2000-01-01
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
Irrational conformal field theory
M. B. Halpern; E. Kiritsis; N. A. Obers; K. Clubok
1996-01-01
This is a review of irrational conformal field theory, which includes rational conformal field theory as a small subspace. Central topics of the review include the Virasoro master equation, its solutions and the dynamics of irrational conformal field theory. Discussion of the dynamics includes the generalized Knizhnik-Zamolodchikov equations on the sphere, the corresponding heat-like systems on the torus and the
Lagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry
Li, Xiaofan
Lagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry #3; Russel E. Ca isch and Xiao-Fan Li Mathematics Department UCLA Los Angeles, CA 90024-1555 USA August 25, 2003 Abstract-dimensional (planar) sheet. This general equation is specialized to sheets with axial or helical symmetry
Lagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry
Caflisch, Russel
Lagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry Russel E. Caflisch and Xiao-Fan-dimensional (planar) sheet. This general equation is specialized to sheets with axial or helical symmetry-dimensional problem. Under the additional assumption of helical or axial symmetry, the problem is further reduced
Lagrangian and Hamiltonian formalism for discontinuous fluid and gravitational field
P. Hajicek; J. Kijowski
1997-07-09
The barotropic ideal fluid with step and delta-function discontinuities coupled to Einstein's gravity is studied. The discontinuities represent star surfaces and thin shells; only non-intersecting discontinuity hypersurfaces are considered. No symmetry (like eg. the spherical symmetry) is assumed. The symplectic structure as well as the Lagrangian and the Hamiltonian variational principles for the system are written down. The dynamics is described completely by the fluid variables and the metric on the fixed background manifold. The Lagrangian and the Hamiltonian are given in two forms: the volume form, which is identical to that corresponding to the smooth system, but employs distributions, and the surface form, which is a sum of volume and surface integrals and employs only smooth variables. The surface form is completely four- or three-covariant (unlike the volume form). The spacelike surfaces of time foliations can have a cusp at the surface of discontinuity. Geometrical meaning of the surface terms in the Hamiltonian is given. Some of the constraint functions that result from the shell Hamiltonian cannot be smeared so as to become differentiable functions on the (unconstrained) phase space. Generalization of the formulas to more general fluid is straifgtforward.
Quantum Field Theory and Representation Theory
Woit, Peter
Quantum Field Theory and Representation Theory Peter Woit woit@math.columbia.edu Department of Mathematics Columbia University Quantum Field Theory and Representation Theory p.1 #12;Outline of the talk · Quantum Mechanics and Representation Theory: Some History Quantum Field Theory and Representation Theory
Tulczyjew Triples in Higher Derivative Field Theory
Katarzyna Grabowska; Luca Vitagliano
2015-02-20
The geometrical structure known as Tulczyjew triple has been used with success in analytical mechanics and first order field theory to describe a wide range of physical systems including Lagrangian/Hamiltonian systems with constraints and/or sources, or with singular Lagrangian. Starting from the first principles of the variational calculus we derive Tulczyjew triples for classical field theories of arbitrary high order, i.e. depending on arbitrary high derivatives of the fields. A first triple appears as the result of considering higher order theories as first order ones with configurations being constrained to be holonomic jets. A second triple is obtained after a reduction procedure aimed at getting rid of nonphysical degrees of freedom. This picture we present is fully covariant and complete: it contains both Lagrangian and Hamiltonian formalisms, in particular the Euler-Lagrange equations. Notice that, the required Geometry of jet bundles is affine (as opposed to the linear Geometry of the tangent bundle). Accordingly, the notions of affine duality and affine phase space play a distinguished role in our picture. In particular the Tulczyjew triples in this paper consist of morphisms of double affine-vector bundles which, moreover, preserve suitable presymplectic structures.
I.Y. Dodin; N.J. Fisch; G.M. Fraiman
2003-02-06
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.
F. I. Mikhail
1964-01-01
Summary A unified field theory is formulated using a tetrad vector field. The field relations are derived by following a procedure\\u000a similar to that used byEinstein in 1951, with the affine connexion being, here, defined in terms of the tetrad field instead of Einstein’s nonsymmetric tensorg\\u000a ??. The suggested field relations are applied to the tetrad field, having spherical symmetry, used
Non-anticommutative supersymmetric field theory and quantum shift
Masato Arai; Masud Chaichian; Kazuhiko Nishijima; Anca Tureanu
2006-01-01
Non-anticommutative Grassmann coordinates in four-dimensional twist-deformed N=1 Euclidean superspace are decomposed into geometrical ones and quantum shift operators. This decomposition leads to the mapping from the commutative to the non-anticommutative supersymmetric field theory. We apply this mapping to the Wess–Zumino model in commutative field theory and derive the corresponding non-anticommutative Lagrangian. Based on the theory of twist deformations of Hopf
Superconformal unified field theory
M. Kaku; P. K. Townsend; P. van Nieuwenhuizen
1977-01-01
We present the gauge theory of the graded conformal group. It contains four real fields with spins 2,3\\/2, 1, and 1\\/2. The theory is invariant under local proper conformal, scale, chiral, gravitational, and supersymmetry transformations. This is the first of a class of superunified field theories, possessing U(n) rather than O(n) internal gauge symmetries and without a cosmological constant. Unitarity,
Ning Wu
1998-06-03
In this paper, we will construct a gauge field model, in which the masses of gauge fields are non-zero and the local gauge symmetry is strictly preserved. A SU(N) gauge field model is discussed in details in this paper. In the limit $\\alpha \\longrightarrow 0$ or $\\alpha \\longrightarrow \\infty$, the gauge field model discussed in this paper will return to Yang-Mills gauge field model. This theory could be regarded as theoretical development of Yang-Mills gauge field theory.
Effective field theory of multi-field inflation a la Weinberg
Nima Khosravi
2012-01-01
We generalise Weinberg's effective field theory approach to multiple-field inflation. In addition to standard terms in the Lagrangian we consider terms containing up to the fourth derivative of the scalar fields and the metric. The results illustrate the possible shapes of the interactions which will yield non-Gaussianity. Generally we find that the speed of sound differs from, but is close
An effective lagrangian for the pure N = 1 supersymmetric Yang-Mills theory
Gabriele Veneziano; Shimon Yankielowicz
1982-01-01
An effective lagrangian for the pure, N=1, supersymmetric Yang-Mills theory is proposed by suitably modifying that of QCD. The quantum breaking of scale and chiral invariance by the corresponding anomalies generates a massive Wess-Zumino supermultiplet while preserving supersymmetry. The large-Nc limit is discussed for an SU(Nc) gauge group. On leave from Tel-Aviv University, Israel. Supported in part by the Bi-National
Attractive Lagrangians for noncanonical inflation
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
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.
Einstein's Unified Field Theory
Behram Kursunoglu
1952-01-01
In this paper it is shown that, under certain assumptions about the metric of the space-time, energy momentum tensor of the total field, when Einstein's field equations are satisfied, vanishes identically.A new version of the unified field theory is suggested, and it is indicated briefly that a genuine energy momentum tensor exists which is conserved and has a structure similar
Matsubara, Takahiko [Department of Physics, Nagoya University, Chikusa, Nagoya, 464-8602 (Japan)
2008-10-15
The nonlinear perturbation theory of gravitational instability is extended to include effects of both biasing and redshift-space distortions, which are inevitable in predicting observable quantities in galaxy surveys. Weakly nonlinear effects in galaxy clustering on large scales recently attracted great interest, since the precise determination of scales of baryon acoustic oscillations is crucial to investigate the nature of dark energy by galaxy surveys. We find that a local Lagrangian bias and redshift-space distortions are naturally incorporated in our formalism of perturbation theory with a resummation technique via the Lagrangian picture. Our formalism is applicable to any biasing scheme which is local in Lagrangian space, including the halo bias as a special case. Weakly nonlinear effects on halo clustering in redshift space are analytically given. We assume only a fundamental idea of the halo model: haloes form according to the extended Press-Schechter theory, and the spatial distributions are locally biased in Lagrangian space. There is no need for assuming the spherical collapse model to follow the dynamical evolution, which is additionally assumed in standard halo prescriptions. One-loop corrections to the power spectrum and correlation function of haloes in redshift space are explicitly derived and presented. Instead of relying on expensive numerical simulations, our approach provides an analytic way of investigating the weakly nonlinear effects, simultaneously including the nonlinear biasing and nonlinear redshift-space distortions. Nonlinearity introduces a weak scale dependence in the halo bias. The scale dependence is a smooth function in Fourier space, and the bias does not critically change the feature of baryon acoustic oscillations in the power spectrum. The same feature in the correlation function is less affected by nonlinear effects of biasing.
(Non-)decoupled supersymmetric field theories
NASA Astrophysics Data System (ADS)
Di Pietro, Lorenzo; Dine, Michael; Komargodski, Zohar
2014-04-01
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).
On p-Adic Sector of Open Scalar Strings and Zeta Field Theory
Dragovich, Branko [Institute of Physics, Pregrevica 118, Zemun, P.O. Box 57, 11001 Belgrade (Serbia)
2010-06-17
We consider construction of Lagrangians which may be suitable for description of p-adic sector of an open scalar string. Such Lagrangians have their origin in Lagrangian for a single p-adic string and they contain the Riemann zeta function with the d'Alembertian in its argument. However, investigation of the field theory with Riemann zeta function is interesting in itself as well. We present a brief review and some new results.
Understanding conformal field theory through parafermions and Chern Simons theory
Hotes, S.A.
1992-11-19
Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.
Free field theory at null infinity and white noise calculus: a BMS invariant dynamical system
Claudio Dappiaggi
2006-07-25
In the context of asymptotically flat spacetimes we exploit techniques proper either of white noise analysis either of dynamical systems in order to develop the Lagrangian and the Hamiltonian approach to a BMS invariant field theory at null infinity.
General relativistic mean field theory for rotating nuclei
Madokoro, Hideki [Department of Physics, Kyushu University, Fukuoka 812-81 (Japan)] Matsuzaki, Masayuki [Department of Physics, Fukuoka University of Education, Munakata, Fukuoka 811-41 (Japan)
1997-12-01
We formulate a general relativistic mean field theory for rotating nuclei starting from the special relativistic {sigma}-{omega} model Lagrangian. The tetrad formalism is adopted to generalize the model to the accelerated frame. {copyright} {ital 1997} {ital The American Physical Society}
Information channel capacity in the field theory estimation
J. S?adkowski; J. Syska
2012-12-26
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.
Effective field theory of gravity for extended objects
Walter D. Goldberger; Ira Z. Rothstein
2006-01-01
Using effective field theory (EFT) methods we present a Lagrangian formalism which describes the dynamics of nonrelativistic extended objects coupled to gravity. The formalism is relevant to understanding the gravitational radiation power spectra emitted by binary star systems, an important class of candidate signals for gravitational wave observatories such as LIGO or VIRGO. The EFT allows for a clean separation
Effective Field Theories from Soft Limits of Scattering Amplitudes
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-01
We derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.
Gauge Theory of the Gravitational-Electromagnetic Field
Robert D. Bock
2015-05-26
We develop a gauge theory of the combined gravitational-electromagnetic field by expanding the Poincar\\'e group to include clock synchronization transformations. We show that the electromagnetic field can be interpreted as a local gauge theory of the synchrony group. According to this interpretation, the electromagnetic field equations possess nonlinear terms and electromagnetic gauge transformations acquire a space-time interpretation as local synchrony transformations. The free Lagrangian for the fields leads to the usual Einstein-Maxwell field equations with additional gravitational-electromagnetic coupling terms. The connection between the electromagnetic field and the invariance properties of the Lagrangian under clock synchronization transformations provides a strong theoretical argument in favor of the thesis of the conventionality of simultaneity. This suggests that clock synchronization invariance (or equivalently, invariance under transformations of the one-way speed of light) is a fundamental invariance principle of physics.
M theory as a holographic field theory
Petr Horava
1999-01-01
We suggest that M theory could be nonperturbatively equivalent to a local quantum field theory. More precisely, we present a ``renormalizable'' gauge theory in eleven dimensions, and show that it exhibits various properties expected of quantum M theory, most notably the holographic principle of 't Hooft and Susskind. The theory also satisfies Mach's principle: A macroscopically large space-time (and the
Algebraic orbifold conformal field theories
Feng Xu
2000-01-01
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
Nonlinear quantum equations: Classical field theory
NASA Astrophysics Data System (ADS)
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-01
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q ? 1. The main characteristic of this field theory consists on the fact that besides the usual ? (x,t), a new field ? (x,t) needs to be introduced in the Lagrangian, as well. The field ? (x,t), which is defined by means of an additional equation, becomes ? ^{*}(x,t) only when q ? 1. The solutions for the fields ? (x,t) and ? (x,t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E2 = p2c2 + m2c4, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
NASA Astrophysics Data System (ADS)
Alles, Alexandre; Buchert, Thomas; Al Roumi, Fosca; Wiegand, Alexander
2015-07-01
The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the first-order trace solutions that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given together with extensions and applications for accessing the nonperturbative regime. We furnish here construction rules to obtain from Newtonian solutions the gravitoelectric class of relativistic solutions, for which we give the complete perturbation and solution schemes at any order of the perturbations. By construction, these schemes generalize the complete hierarchy of solutions of the Newtonian Lagrangian perturbation theory.
Beyond mean field theory: statistical field theory for neural networks
Buice, Michael A; Chow, Carson C
2014-01-01
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014
Perturbation density functional theory for nonuniform fluid mixture based on Lagrangian theorem
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
2004-02-01
First order direct correlation function (DCF) of non-uniform fluid mixture was expanded around the bulk fluid mixture, the expansion was truncated at the lowest order and made formally exact by making use of functional counterpart of Lagrangian theorem of differential calculus. The concrete procedure involves the specification of the non-uniform component i-component j pair second order DCF by their respective uniform counterpart with appropriate weighted packing fraction and weighted concentration as their arguments. As an example, the truncated expansion was incorporated into the density functional theory (DFT) formalism to predict the density profile of binary hard sphere fluid near a structureless hard wall. Good agreement between theoretical predictions and simulation data demonstrates the reliable accuracy of the present approach.
Towards a double field theory on para-Hermitian manifolds
Vaisman, Izu [Department of Mathematics, University of Haifa, Haifa (Israel)] [Department of Mathematics, University of Haifa, Haifa (Israel)
2013-12-15
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.
Quantum Knots and New Quantum Field Theory
Sze Kui Ng
2013-05-10
We propose a new gauge theory of quantum electrodynamics (QED) and quantum chromodynamics (QCD) from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from quantum field theory based on the Chern-Simon Lagrangian. From our approach we can derive new knot invariants which extend the Jones polynomial and give a complete classification of knots. We model elementary particles by quantum knots. From the construction of quantum knots we construct quantum photon propagator and quantum gloun propagator for the nuclear force beween elementary particles. Then from the propagators a renormalization group equation is derived for the critical phenomena of QED and QCD of electrons and quarks including superconductivity and color superconductivity.
Dynamical torsion in a gravitational theory coupled to first-order twist-tensor matter fields
Rosenbaum, M.; Ryan, M.P. Jr.; Urrutia, L.F.; Luehr, C.P.
1982-08-15
A gravity-matter theory is developed using twist tensors as bona fide matter fields which are minimally coupled to gravitation by means of a first-order matter Lagrangian. The main features of the theory are (i) torsion is generated dynamically by the matter fields and (ii) torsion is coupled to a scalar field via a nonzero spin density which arises from the first-order matter Lagrangian but nevertheless provides a vanishing integrated spin for the scalar field. The equations of motion for the fields are given and some solutions are discussed.
Unified Field Theories Hitoshi Murayama
Murayama, Hitoshi
Unified Field Theories Hitoshi Murayama Department of Physics, University of California Berkeley This article explains the idea of unified field theories in particle physics. It starts with a historical review of two successful theories which unified two apparently distinct forces: Maxwell's theory
Dmitriy Palatnik
2005-08-12
Suggested modification of the Einstein-Maxwell system, such that Maxwell equations become non-gauge and nonlinear. The theory is based on assumption that observable (i.e., felt by particles) metric is $ {\\tilde{g}}_{ab} = g_{ab} - l^2{A}_a{A}_b$, where $g_{ab}$ is metric (found from Einstein equations), $A_a$ is electromagnetic potential, and $l$ is fundamental constant of the theory. Specific model of the mass and charge densities of a fundamental particle is considered. As a result, one obtains solutions corresponding to quantized electrical charge with spectrum $q_{n} = {{2n}\\over3}e$ and $q'_{n} = -{(2n+1)\\over3}e$, where $n = 0, 1, 2, ...$ Theory predicts Coulomb interaction between electrical charges and masses. Namely, if ($m, e$) and ($m',e'$) describe masses and electrical charges of two particles respectively, then energy of interaction (in non-relativistic limit) is $V(r) = [ee' - kmm' - \\sqrt k(em' + e'm)]/r$. It follows, then, that the Earth's mass, $M_E$, contributes negative electrical charge, $Q_E = - \\sqrt k M_E$, which explains why primary cosmic rays consist mainly of positively charged particles. One may attribute the fairweather electric field at the Earth's surface to the charge $Q_E$.
Altimetric lagrangian advection to reconstruct Pacific Ocean fine scale surface tracer fields
NASA Astrophysics Data System (ADS)
Rogé, Marine; Morrow, Rosemary; Dencausse, Guillaume
2015-04-01
In past studies, lagrangian stirring of surface tracer fields by altimetric surface geostrophic currents has been performed in different mid to high-latitude regions, showing good results in reconstructing finer-scale tracer patterns. Here we apply the technique to three different regions in the eastern and western tropical Pacific, and in the subtropical southwest Pacific. Initial conditions are derived from weekly gridded temperature and salinity fields, based on hydrographic data and Argo. Validation of the improved fine-scale surface tracer fields is performed using satellite AMSRE SST data, and high-resolution ship thermosalinograph data. We test two kinds of lagrangian advection. The standard one-way advection is shown to introduce an increased tracer bias as the advection time increases. Indeed, since we only use passive stirring, a bias is introduced from the missing physics, such as air-sea fluxes or mixing. A second "backward-forward" advection technique is shown to reduce the seasonal bias, but more data is lost around coasts and islands, a strong handicap in the tropical Pacific with many small islands. In the subtropical Pacific Ocean, the mesoscale temperature and salinity fronts are well represented by the one-way advection over a 10-day advection time, including westward propagating features not apparent in the initial fields. In the tropics, the results are less clear. The validation is hampered by the complex vertical stratification, and the technique is limited by the lack of accurate surface currents for the stirring - the gridded altimetric fields poorly represent the meridional currents, and are not detecting the fast tropical instability waves, nor the wind-driven circulation. We suggest that the passive lateral stirring technique is efficient in regions with moderate the high mesoscale energy and correlated mesoscale surface temperature and surface height. In other regions, more complex dynamical processes may need to be included.
Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field
Yuri N. Obukhov; Tomas Ramos; Guillermo F. Rubilar
2012-09-13
We develop a relativistic variational model for a nematic liquid crystal interacting with an electro- magnetic field. The constitutive relation for a general anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss light wave propagation in this moving uniaxial medium, for which the corresponding optical metrics are identified explicitly. A Lagrangian for the coupled system of a nematic liquid crystal and the electromagnetic field is constructed, from which a complete set of equations of motion for the system is derived. The canonical energy-momentum and spin tensors are systematically obtained. We compare our results with those within the non-relativistic models. As an application of our general formalism, we discuss the so-called Abraham-Minkowski controversy on the momentum of light in a medium.
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields. PMID:25763950
Geometrical structures of higher-order dynamical systems and field theories
Pedro D. Prieto-Martínez
2014-10-28
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian function/density, or a Hamiltonian that admits Lagrangian counterpart. These geometric frameworks are used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems in field theory.
Screening of scalar fields in Dirac-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Burrage, Clare; Khoury, Justin
2014-07-01
We study a new screening mechanism which is present in Dirac-Born-Infeld (DBI)-like theories. A scalar field with a DBI-like Lagrangian is minimally coupled to matter. In the vicinity of sufficiently dense sources, nonlinearities in the scalar dominate and result in an approximately constant acceleration on a test particle, thereby suppressing the scalar force relative to gravity. Unlike generic P(X) or chameleon theories, screening happens within the regime of validity of the effective field theory thanks to the DBI symmetry. We derive an exact form for the field profile around multiple sources and determine the constraints on the theory parameters from tests of gravity. Perturbations around the spherically-symmetric background propagate superluminally, but we argue for a chronology protection analogous to Galileons. This is the first example of a screening mechanism for which quantum corrections to the theory are under control and exact solutions to cosmological N-body problems can be found.
Noncommutative field theories and gravity
Victor O. Rivelles; Caixa Postal
2003-01-01
We show that after the Seiberg–Witten map is performed the action for noncommutative field theories can be regarded as a coupling to a field dependent gravitational background. This gravitational background depends only on the gauge field. Charged and uncharged fields couple to different backgrounds and we find that uncharged fields couple more strongly than the charged ones. We also show
Nonlinear quantum equations: Classical field theory
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
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.
What is the simplest quantum field theory?
Nima Arkani-Hamed; Freddy Cachazo; Jared Kaplan
2010-01-01
Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation theory. An ever-increasing\\u000a understanding of the structure of scattering amplitudes has however been pointing to the opposite conclusion. At tree level,\\u000a the BCFW recursion relations that completely determine the S-matrix are valid not for scalar theories but for gauge theories\\u000a and gravity, with gravitational amplitudes
A Lagrangian description of nearshore hydrodynamics and rip currents forced by a random wave field
NASA Astrophysics Data System (ADS)
Leandro, S.; Cienfuegos, R.; Escauriaza, C. R.
2011-12-01
Nonlinear processes become important for waves propagating in the shoaling and surf zones. Wave shape changes when approaching the coast under the influence of bathymetry, becoming increasingly asymmetric until reaching the breaking limit. In the shoaling zone, non-linearities induce a net velocity in the direction of wave propagation, a phenomenon called Stokes drift, while in the surf zone, currents are mainly driven by spatio-temporal variations in energy dissipation gradients. In this work we aim at investigating and characterizing the nearshore circulation forced by a random wave field propagating over a variable bathymetry. We carry out numerical simulations over a laboratory experiment conducted in a wave basin over a realistic bathymetry [Michallet et al. 2010]. For the hydrodynamics, we use a 2D shock-capturing finite-volume model that solves the non-linear shallow water equations, taking into account energy dissipation by breaking, friction, bed-slope variations, and an accurate description for the moving shoreline in the swash zone [Marche et al. 2007;Guerra et al. 2010]. Model predictions are compared and validated against experimental data giving confidence for its use in the description of wave propagation in the surf/swash zone, together with mean eulerian velocities. The resulting wave propagation and circulation provided by the 2D model will then be used to describe drifter's patterns in the surf zone and construct Lagrangian particle tracking. The chosen experimental configuration is of great interest due to the random wave forcing (slowly modulated), the beach non-uniformities, and the existence of several bar-rip channels that enhance quasi-periodic rip instabilities. During the experiment, balloons filled with water, with a diameter between 5 and 10 cm, were placed in the surf zone in order to characterize circulation in a Lagrangian framework [Castelle et al. 2010]. The time-location of the balloons was continuously tracked by a shore-mounted video camera, and the images were processed to obtain the trajectories and mean velocities. The Lagrangian description provided by the numerical model will be thus confronted to experimental data, and then used to characterize circulation patterns, rip instabilities and infragravity wave pulsations.
The Supersymmetry Soft-breaking Lagrangian - Where Experiment and String Theory Meet
Gordon L. Kane
2000-08-29
After an introduction recalling that we expect low energy supersymmetry to be part of our description of nature because of considerable indirect evidence and successful predictions, and a discussion of the essential role of data for formulating and testing string theory, these lectures focus on the role of the supersymmetry soft-breaking Lagrangian in connecting experiment and string theory. How to measure tan$\\beta$ and the soft parameters is examined via a number of applications, and the difficulty of measuring tan$\\beta$ at hadron colliders is explained. In each case the important role of soft phases is made explicit, and the true number of parameters is counted. Applications include the chargino and neutralino sectors, the Higgs sector and how its results change when phases are included, measuring the (relative) gluino phase, CP violation in K and B systems and whether all CP violation can be due to soft phases, how to learn if the LSP is the cold dark matter of the universe, and baryogenesis. It is emphasized that the success of supersymmetry in explaining the breaking of electroweak symmetry is probably its most important achievement, and implications of that explanation for superpartner masses are shown. Combining many of these considerations, a further application argues that a lepton collider of total energy 600 GeV with a polarized beam is one we can be confident will do important physics even after LHC. The question of the origins of CP violation, whether the CKM phase can be zero, and the possibility that the soft phases can tell us about compactification and supersymmetry breaking are discussed. Some of the applications and issues are examined in a D-brane based model that can describe the usual collider and dark matter phenomenology, and includes phases and CP violation as well.
Vector field theories in cosmology
A. Tartaglia; N. Radicella
2007-08-05
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, whilst other vector theories use much more. The Newtonian limits are also compared. Finally we show that the CD theory may be considered as a special case of the aether theories, corresponding to a more compact and consistent paradigm.
Field theory and particle physics
Eboli, O.J.P.; Gomes, M.; Santoro, A.
1990-01-01
This book contains the proceedings of the topics covered during the fifth Jorge Andre Swieca Summer School. The first part of the book collects the material devoted to quantum field theory. There were four courses on methods in Field Theory; H. O. Girotti lectured on constrained dynamics, R. Jackiw on the Schrodinger representation in Field Theory, S.-Y. Pi on the application of this representation to quantum fields in a Robertson-Walker spacetime, and L. Vinet on Berry Connections. There were three courses on Conformal Field Theory: I. Todorov focused on the problem of construction and classification of conformal field theories. Lattice models, two-dimensional S matrices and conformal field theory were looked from the unifying perspective of the Yang-Baxter algebras in the lectures given by M. Karowski. Parasupersymmetric quantum mechanics was discussed in the lectures by L. Vinet. Besides those courses, there was an introduction to string field theory given by G. Horowitz. There were also three seminars: F. Schaposnik reported on recent applications of topological methods in field theory, P. Gerbert gave a seminar on three dimensional gravity and V. Kurak talked on two dimensional parafermionic models. The second part of this proceedings is devoted to phenomenology. There were three courses on Particle Physics: Dan Green lectured on collider physics, E. Predrazzi on strong interactions and G. Cohen-Tanoudji on the use of strings in strong interactions.
Aspects of affine Toda field theory
Corrigan, E. (Durham Univ. (United Kingdom))
1992-06-01
This paper describes affine Toda field theory which is a theory of r scalar fields in two-dimensional Minkowski space-time, where r is the rank of a compact semi-simple Lie algebra g. The classical field theory is determined by the lagrangian density L = 1/2 {partial derivative}{sub {rho}}{phi}{sup a}{partial derivative}{sup {mu}}{phi}{sup a} {minus} V({phi}) where V({phi}) = m{sup 2}/{beta}{sup 2} {Sigma}{sub 0}{sup r}n{sub i}e{sup {beta}{alpha}{sub i} {center dot} {phi}}. m and {beta} are real, classically unimportant constants, {alpha}{sub i} i = 1, . . . ,r are the simple roots of the Lie algebra g, and {alpha}{sub 0} = {Sigma}{sub 1}{sup 4} n{alpha}{sub i} is a linear combination of the simple roots; it corresponds to the extra spot on an extended Dynkin diagram for g. A reasonable question to ask is whether the classical integrability survives into the quantum field theory and, if so, what is the spectrum and to what extent is it possible to calculate explicitly quantities of interest such as S-matrices and form factors. The recent discoveries leave no doubt that these relatively simple models have much structure and their study (even in the {beta}{sup 2} {gt} 0 regime) will be informative. In this short review, the ADE series of Lie algebras will be singled out for special attention.
NASA Astrophysics Data System (ADS)
Kwak, Seung Ki
The existence of momentum and winding modes of closed string on a torus leads to a natural idea that the field theoretical approach of string theory should involve winding type coordinates as well as the usual space-time coordinates. Recently developed double field theory is motivated from this idea and it implements T-duality manifestly by doubling the coordinates. In this thesis we will mainly focus on the double field theory formulation of different string theories in its low energy limit: bosonic, heterotic, type II and its massive extensions, and N = 1 supergravity theory. In chapter 2 of the thesis we study the equivalence of different formulations of double field theory. There are three different formulations of double field theory: background field E formulation, generalized metric H formulation, and frame field EAM formulation. Starting from the frame field formalism and choosing an appropriate gauge, the equivalence of the three formulations of bosonic theory are explicitly verified. In chapter 3 we construct the double field theory formulation of heterotic strings. The global symmetry enlarges to O( D, D + n) for heterotic strings and the enlarged generalized metric features this symmetry. The structural form of bosonic theory can directly be applied to the heterotic theory with the enlarged generalized metric. In chapter 4 we develop a unified framework of double field theory for type II theories. The Ramond-Ramond potentials fit into spinor representations of the duality group O( D, D) and the theory displays Spin+( D, D) symmetry with its self-duality relation. For a specific form of RR 1-form the theory reduces to the massive deformation of type IIA theory due to Romans. In chapter 5 we formulate the N = 1 supersymmetric extension of double field theory including the coupling to n abelian vector multiplets. This theory features a local O(1, 9 + n) x O(1, 9) tangent space symmetry under which the fermions transform. (Copies available exclusively from MIT Libraries, libraries.mit.edu/docs - docs mit.edu)
Lectures on 2D yang-mills theory, equivariant cohomology and topological field theories
Stefan Cordes; Gregory Moore; Sanjaye Ramgoolam
1995-01-01
These are expository lectures reviewing\\u000a (1) recent developments in two-dimensional Yang-Mills theory, and\\u000a (2) the construction of topological field theory Lagrangians. Topological\\u000afield theory is discussed from the point of view of infinite-dimensional\\u000adifferential geometry. We emphasize the unifying role of equivariant cohomology\\u000aboth as the underlying principle in the formulation of BRST transformation laws\\u000aand as a central concept
Roel Snieder; Evert Slob; Kees Wapenaar
2010-01-01
The extraction of the response of physical systems from field fluctuations is an area undergoing rapid growth. It is of relevance because it makes it possible to obtain the response of the system from passive field fluctuations instead of from an active point source. The impulse response is characterized by the Green's function G(t). The existing theory leads to the
NASA Astrophysics Data System (ADS)
Townsend, Paul K.
2005-03-01
Starting with intersecting M2-branes in M-theory, the IIA supertube can be found by S compactification followed by a boost to the speed of light in the 11th dimension. A similar procedure applied to Donaldson-Uhlenbeck-Yau instantons on C, viewed as intersecting membranes of D=7 supersymmetric Yang-Mills (SYM) theory, yields (for finite boost) a new set of 1/4 BPS equations for D=6 SYM-Higgs theory, and (for infinite boost) a generalization of the dyonic instanton equations of D=5 SYM-Higgs theory, solutions of which are interpreted as Yang-Mills supertubes and realized as configurations of IIB string theory. To cite this article: P.K. Townsend, C. R. Physique 6 (2005).
NASA Astrophysics Data System (ADS)
Kord, A. F.; Haddadi Moghaddam, M.; Ghasempour, N.
2015-04-01
We investigate some issues on renormalisability of non-anticommutative supersymmetric gauge theory related to field redefinitions. We study one loop corrections to N =1/2 supersymmetric SU (N) × U (1) gauge theory coupled to chiral matter in component formalism, and show the procedure which has been introduced for renormalisation is problematic because some terms which are needed for the renormalisability of theory are missed from the Lagrangian. In order to prove the theory is renormalisable, we redefine the gaugino and the auxiliary fields (? , F bar), which result in a modified form of the Lagrangian in the component formalism. Then, we show the modified Lagrangian has extra terms which are necessary for renormalisability of non-anticommutative supersymmetric gauge field theories. Finally, we prove N =1/2 supersymmetric gauge theory is renormalisable up to one loop corrections using standard method of renormalisation; besides, it is shown the effective action is gauge invariant.
Little String Theory from Double-Scaling Limits of Field Theories
Henry Ling; Hsien-Hang Shieh; Greg van Anders
2006-11-25
We show that little string theory on S^5 can be obtained as double-scaling limits of the maximally supersymmetric Yang-Mills theories on RxS^2 and RxS^3/Z_k. By matching the gauge theory parameters with those in the gravity duals found by Lin and Maldacena, we determine the limits in the gauge theories that correspond to decoupling of NS5-brane degrees of freedom. We find that for the theory on RxS^2, the 't Hooft coupling must be scaled like ln^3(N), and on RxS^3/Z_k, like ln^2(N). Accordingly, taking these limits in these field theories gives Lagrangian definitions of little string theory on S^5.
Thomas Buchert
1993-09-30
The Lagrangian perturbation theory on Friedman-Lemaitre cosmologies investigated and solved up to the second order in earlier papers (Buchert 1992, Buchert \\& Ehlers 1993) is evaluated up to the third order. On its basis a model for non-linear clustering applicable to the modeling of large-scale structure in the Universe for generic initial conditions is formulated. A truncated model is proposed which represents the ``main body'' of the perturbation sequence in the early non-linear regime by neglecting all gravitational sources which describe interaction of the perturbations. However, I also give the irrotational solutions generated by the interaction terms to the third order, which induce vorticity in Lagrangian space. The consequences and applicability of the solutions are put into perspective. In particular, the model presented enables the study of previrialization effects in gravitational clustering and the onset of non-dissipative gravitational turbulence within the cluster environment.
Paul K. Townsend
2005-01-01
Starting with intersecting M2-branes in M-theory, the IIA supertube can be found by S1 compactification followed by a boost to the speed of light in the 11th dimension. A similar procedure applied to Donaldson–Uhlenbeck–Yau instantons on C3, viewed as intersecting membranes of D=7 supersymmetric Yang–Mills (SYM) theory, yields (for finite boost) a new set of 1\\/4 BPS equations for D=6
Paul K. Townsend
2005-01-01
Starting with intersecting M2-branes in M-theory, the IIA supertube can be found by S compactification followed by a boost to the speed of light in the 11th dimension. A similar procedure applied to Donaldson Uhlenbeck Yau instantons on C, viewed as intersecting membranes of D=7 supersymmetric Yang Mills (SYM) theory, yields (for finite boost) a new set of 1\\/4 BPS
Towards effective Lagrangians for adelic strings
Branko Dragovich
2009-02-02
p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By this way, one can consider adelic strings as a very useful instrument in the further investigation of modern string theory. It is remarkable that for some scalar p-adic strings exist effective Lagrangians, which are based on real instead of p-adic numbers and describe not only four-point scattering amplitudes but also all higher ones at the tree level. In this work, starting from p-adic Lagrangians, we consider some approaches to construction of effective field Lagrangians for p-adic sector of adelic strings. It yields Lagrangians for nonlinear and nonlocal scalar field theory, where spacetime nonlocality is determined by an infinite number of derivatives contained in the operator-valued Riemann zeta function. Owing to the Riemann zeta function in the dynamics of these scalar field theories, obtained Lagrangians are also interesting in themselves.
Gravity From Topological Field Theory
J. Gegenberg; R. B. Mann
1999-02-04
We construct a topological field theory which, on the one hand, generalizes BF theories in that there is non-trivial coupling to `topological matter fields'; and, on the other, generalizes the three-dimensional model of Carlip and Gegenberg to arbitrary dimensional manifolds. Like the three dimensional model, the theory can be considered to describe a gravitational field interacting with topological matter. In particular, in two dimensions, the model is that of gravity on a torus. In four dimensions, the model is shown to admit constant curvature black hole solutions.
Double Field Theory at Order $?'$
Olaf Hohm; Barton Zwiebach
2014-08-06
We investigate $\\alpha'$ corrections of bosonic strings in the framework of double field theory. The previously introduced "doubled $\\alpha'$-geometry" gives $\\alpha'$-deformed gauge transformations arising in the Green-Schwarz anomaly cancellation mechanism but does not apply to bosonic strings. These require a different deformation of the duality-covariantized Courant bracket which governs the gauge structure. This is revealed by examining the $\\alpha'$ corrections in the gauge algebra of closed string field theory. We construct a four-derivative cubic double field theory action invariant under the deformed gauge transformations, giving a first glimpse of the gauge principle underlying bosonic string $\\alpha'$ corrections. The usual metric and $b$-field are related to the duality covariant fields by non-covariant field redefinitions.
California at Santa Cruz, University of
) - V (# + #) , (11) where the potential function V is a function of # + i # i . Such a theory in terms of hermitian fields # Ai and #Bi defined by: # j = 1 # 2 (# Aj + i# Bj ) , # + j = 1 # 2 (# Aj - i
Crystal field theory with covalency
B. R. Russell; R. M. Hedges
1970-01-01
The use of a covalency parameter in Crystal Field Theory calculations has been applied to sixteen octahedral complexes. The variables fitted to experiment have been correlated to theoretical parameters.
Kwak, Seung Ki
2012-01-01
The existence of momentum and winding modes of closed string on a torus leads to a natural idea that the field theoretical approach of string theory should involve winding type coordinates as well as the usual space-time ...
Double field theory at order ??
Hohm, Olaf
We investigate ?? corrections of bosonic strings in the framework of double field theory. The previously introduced “doubled ??-geometry” gives ??-deformed gauge transformations arising in the Green-Schwarz anomaly ...
Group Field Theory: An Overview
Laurent Freidel
2005-01-01
We give a brief overview of the properties of a higher-dimensional generalization of matrix model which arise naturally in the context of a background approach to quantum gravity, the so-called group field theory. We show in which sense this theory provides a third quantization point-of-view on quantum gravity.
The $\\hbar$ Expansion in Quantum Field Theory
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
NASA Astrophysics Data System (ADS)
Sheth, Ravi K.; Chan, Kwan Chuen; Scoccimarro, Román
2013-04-01
Halos are biased tracers of the dark matter distribution. It is often assumed that the initial patches from which halos formed are locally biased with respect to the initial fluctuation field, meaning that the halo-patch fluctuation field can be written as a Taylor series in the dark matter density fluctuation field. If quantities other than the local density influence halo formation, then this Lagrangian bias will generically be nonlocal; the Taylor series must be performed with respect to these other variables as well. We illustrate the effect with Monte Carlo simulations of a model in which halo formation depends on the local shear (the quadrupole of perturbation theory) and provide an analytic model that provides a good description of our results. Our model, which extends the excursion set approach to walks in more than one dimension, works both when steps in the walk are uncorrelated, as well as when there are correlations between steps. For walks with correlated steps, our model includes two distinct types of nonlocality: one is due to the fact that the initial density profile around a patch which is destined to form a halo must fall sufficiently steeply around it—this introduces k dependence to even the linear bias factor, but otherwise only affects the monopole of the clustering signal. The other type of nonlocality is due to the surrounding shear field; this affects the quadratic and higher-order bias factors and introduces an angular dependence to the clustering signal. In both cases, our analysis shows that these nonlocal Lagrangian bias terms can be significant, particularly for massive halos; they must be accounted for in, e.g., analyses of higher-order clustering in Lagrangian or Eulerian space. Comparison of our predictions with measurements of the halo bispectrum in simulations is encouraging. Although we illustrate these effects using halos, our analysis and conclusions also apply to the other constituents of the cosmic web—filaments, sheets and voids.
Teleparallel Lagrange Geometry and a Unified Field Theory
M. I. Wanas; Nabil L. Youssef; A. M. Sid-Ahmed
2010-02-13
In this paper, we construct a field theory unifying gravity and electromagnetism in the context of Extended Absolute Parallelism (EAP-) geometry. This geometry combines, within its structure, the geometric richness of the tangent bundle and the mathematical simplicity of Absolute Parallelism (AP-) geometry. The constructed field theory is a generalization of the Generalized Field Theory (GFT) formulated by Mikhail and Wanas. The theory obtained is purely geometric. The horizontal (resp. vertical) field equations are derived by applying the Euler-Lagrange equations to an appropriate horizontal (resp. vertical) scalar Lagrangian. The symmetric part of the resulting horizontal (resp. vertical) field equations gives rise to a generalized form of Einstein's field equations in which the horizontal (resp. vertical) energy-momentum tensor is purely geometric. The skew-symmetric part of the resulting horizontal (resp. vertical) field equations gives rise to a generalized form of Maxwell equations in which the electromagnetic field is purely geometric. Some interesting special cases, which reveal the role of the nonlinear connection in the obtained field equations, are examined. Finally, the condition under which our constructed field equations reduce to the GFT is explicitly established.
Peter O. Hess; Walter Greiner
2007-05-09
A new formulation of field theory is presented, based on a pseudo-complex description. An extended group structure is introduced, implying a minimal scalar length, rendering the theory regularized a la Pauli-Villars. Cross sections are calculated for the scattering of an electron at an external Coulomb field and the Compton scattering. Deviations due to a smallest scalar length are determined. The theory also permits a modification of the minimal coupling scheme, resulting in a generalized dispersion relation. A shift of the Greisen-Zatsepin-Kuzmin-limit (GZK) of the cosmic ray spectrum is the consequence.
Geometer energy unified field theory
NASA Astrophysics Data System (ADS)
Rivera, Susana; Rivera, Anacleto
GEOMETER - ENERGY UNIFIED FIELD THEORY Author: Anacleto Rivera Nivón Co-author: Susana Rivera Cabrera This work is an attempt to find the relationship between the Electromagnetic Field and the Gravitational Field. Despite it is based on the existence of Strings of Energy, it is not the same kind of strings that appears on other theories like Superstring Theory, Branas Theory, M - Theory, or any other related string theories. Here, the Strings are concentrated energy lines that vibrates, and experiences shrinking and elongations, absorbing and yielding on each contraction and expansion all that is found in the Universe: matter and antimatter, waves and energy in all manifestations. In contrast to superstring theory, which strings are on the range of the Length of Planck, these Strings can be on the cosmological size, and can contain many galaxies, or clusters, or groups of galaxies; but also they can reach as small sizes as subatomic levels. Besides, and contrary to what it is stated in some other string theories that need the existence of ten or more dimensions, the present proposal sustains in only four particular dimensions. It has been developed a mathematical support that will try to help to improve the understanding of the phenomena that take place at the Universe.
Positive Topological Quantum Field Theories
Markus Banagl
2013-03-18
We propose a new notion of positivity for topological field theories (TFTs), based on S. Eilenberg's concept of completeness for semirings. We show that a complete ground semiring, a system of fields on manifolds and a system of action functionals on these fields determine a positive TFT. The main feature of such a theory is a semiring-valued topologically invariant state sum that satisfies a gluing formula. The abstract framework has been carefully designed to cover a wide range of phenomena. For instance, we derive Polya's counting theory in combinatorics from state sum identities in a suitable positive TFT. Several other concrete examples are discussed, among them Novikov signatures of fiber bundles over spacetimes and arithmetic functions in number theory. In the future, we will employ the framework presented here in constructing a new differential topological invariant that detects exotic smooth structures on spheres.
Quantum field theory without divergences
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
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.
Spherically-symmetric gravitational fields in the metric-affine gauge theory of gravitation
A. V. Minkevich; Yu. G. Vasilevski
2003-01-24
Geometric structure of spherically-symmetric space-time in metric-affine gauge theory of gravity is studied. Restrictions on curvature tensor and Bianchi identities are obtained. By using certain simple gravitational Lagrangian the solution of gravitational equations for vacuum spherically-symmetric gravitational field is obtained.
Symmetries, sum rules and constraints on effective field theories
NASA Astrophysics Data System (ADS)
Bellazzini, Brando; Martucci, Luca; Torre, Riccardo
2014-09-01
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the scattering amplitudes in the IR to total cross sections integrated all the way up to the UV. Exploiting the group structure of the symmetry, we systematically determine all the independent sum rules and positivity conditions on the expansion coefficients. For effective field theories the amplitudes in the IR are calculable and hence the sum rules set constraints on the parameters of the effective Lagrangian. We clarify the impact of gauging on the sum rules for Goldstone bosons in spontaneously broken gauge theories. We discuss explicit examples that are relevant for WW-scattering, composite Higgs models, and chiral perturbation theory. Certain sum rules based on custodial symmetry and its extensions provide constraints on the Higgs boson coupling to the electroweak gauge bosons.
Symmetries, Sum Rules and Constraints on Effective Field Theories
Brando Bellazzini; Luca Martucci; Riccardo Torre
2014-07-09
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the scattering amplitudes in the IR to total cross sections integrated all the way up to the UV. Exploiting the group structure of the symmetry, we systematically determine all the independent sum rules and positivity conditions on the expansion coefficients. For effective field theories the amplitudes in the IR are calculable and hence the sum rules set constraints on the parameters of the effective Lagrangian. We clarify the impact of gauging on the sum rules for Goldstone bosons in spontaneously broken gauge theories. We discuss explicit examples that are relevant for WW-scattering, composite Higgs models, and chiral perturbation theory. Certain sum rules based on custodial symmetry and its extensions provide constraints on the Higgs boson coupling to the electroweak gauge bosons.
Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect
E. Cremmer; Sergio Ferrara; L. Girardello; A. van Proeyen
1983-01-01
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
The effective field theory of inflation/dark energy and the Horndeski theory
Shinji Tsujikawa
2014-09-01
The effective field theory (EFT) of cosmological perturbations is a useful framework to deal with the low-energy degrees of freedom present for inflation and dark energy. We review the EFT for modified gravitational theories by starting from the most general action in unitary gauge that involves the lapse function and the three-dimensional geometric scalar quantities appearing in the Arnowitt-Deser-Misner (ADM) formalism. Expanding the action up to quadratic order in the perturbations and imposing conditions for the elimination of spatial derivatives higher than second order, we obtain the Lagrangian of curvature perturbations and gravitational waves with a single scalar degree of freedom. The resulting second-order Lagrangian is exploited for computing the scalar and tensor power spectra generated during inflation. We also show that the most general scalar-tensor theory with second-order equations of motion-Horndeski theory-belongs to the action of our general EFT framework and that the background equations of motion in Horndeski theory can be conveniently expressed in terms of three EFT parameters. Finally we study the equations of matter density perturbations and the effective gravitational coupling for dark energy models based on Horndeski theory, to confront the models with the observations of large-scale structures and weak lensing.
Tail terms in gravitational radiation reaction via effective field theory
S. Foffa; R. Sturani
2012-12-24
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 re-produce 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.
Field-theory methods in coagulation theory
Lushnikov, A. A., E-mail: alex.lushnikov@mail.ru [Karpov Institute of Physical Chemistry (Russian Federation)
2011-08-15
Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W(Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = (n{sub 1}, n{sub 2}, ..., n{sub g}, ...), where n{sub g} is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional {Psi} for the probability W(Q, t). The time evolution of {Psi} is described by an equation that is similar to the Schroedinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.
Lagrangian description of warm plasmas
NASA Technical Reports Server (NTRS)
Kim, H.
1970-01-01
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.
An effective-field-theory analysis of low-energy parity-violation in nucleon–nucleon scattering
Daniel R. Phillips; Matthias R. Schindler; Roxanne P. Springer
2009-01-01
We analyze parity-violating nucleon–nucleon scattering at energies Em?2\\/M using the effective field theory appropriate for this regime. The minimal Lagrangian for short-range parity-violating NN interactions is written in an operator basis that encodes the five partial-wave transitions that dominate at these energies. We calculate the leading-order relationships between parity-violating NN asymmetries and the coefficients in the Lagrangian and also discuss
Braided Quantum Field Theories and Their Symmetries
Yuya Sasai; Naoki Sasakura
2007-01-01
Braided quantum field theories, proposed by Oeckl, can provide a framework for quantum field theories that possess Hopf algebra symmetries. In quantum field theories, symmetries lead to non-perturbative relations among correlation functions. We study Hopf algebra symmetries and such relations in the context of braided quantum field theories. We give the four algebraic conditions among Hopf algebra symmetries and braided
Gravitational radiative corrections from effective field theory
Goldberger, Walter D.; Ross, Andreas [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States)
2010-06-15
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.
Introduction to string theory and conformal field theory
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
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.
Quantum Field Theory in Graphene
I. V. Fialkovsky; D. V. Vassilevich
2011-11-18
This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.
Supercomputers and quantum field theory
Creutz, M.
1985-01-01
A review is given of why recent simulations of lattice gauge theories have resulted in substantial demands from particle theorists for supercomputer time. These calculations have yielded first principle results on non-perturbative aspects of the strong interactions. An algorithm for simulating dynamical quark fields is discussed. 14 refs.
A unitary and causal effective field theory
Gasparyan, A. M. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt (Germany); SSC RF ITEP, Bolshaya Cheremushkinskaya 25, 117218 Moscow (Russian Federation); Lutz, M. F. M. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt (Germany)
2011-10-24
We report on a novel scheme based on the chiral Lagrangian. It is used to analyze pion-nucleon scattering, pion photoproduction, and nucleon Compton scattering. Subthreshold partial-wave amplitudes are calculated in chiral perturbation theory and analytically extrapolated with constraints imposed by electromagnetic-gauge invariance, causality and unitarity. Experimental quantities are reproduced up to energies {radical}(s){approx_equal}1300 MeV in terms of the parameters relevant at order Q{sup 3}.
On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory
NASA Technical Reports Server (NTRS)
Vandommelen, Leon L.; Cowley, Stephen J.
1989-01-01
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.
Large N limit of orbifold field theories
Michael Bershadsky; Andrei Johansen
1998-01-01
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
N. Nakazawa
1995-08-22
We apply stochastic quantization method to matrix models for the second quantization of loops in both discretized and continuum levels. The fictitious time evolution described by the Langevin equation is interpreted as the time evolution in a field theory of loops. The corresponding Fokker-Planck hamiltonian defines a non-critical string field theory. We study both orientable and non-orientable interactions of loops in terms of matrix models and take the continuum limit for one-matrix case. As a consequence, we show the equivalence of stochastic quantization of matrix models in loop space to the transfer-matrix formalism in dynamical triangulation of random surfaces. We also clarifies the origin of Virasoro algebra in this context.
Diffeomorphisms in group field theories
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
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.
Symplectic Clifford Algebraic Field Theory.
NASA Astrophysics Data System (ADS)
Dixon, Geoffrey Moore
We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.
Screw dislocations in the field theory of elastoplasticity
NASA Astrophysics Data System (ADS)
Lazar, Markus
2002-10-01
A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely long screw dislocation in a cylinder, a dipole of screw dislocations and a coaxial screw dislocation in a finite cylinder. The stress fields have no singularities in the dislocation core and they are modified in the core due to the presence of localized moment stress. Additionally, we calculated the elastoplastic energies for the screw dislocation in a cylinder and the coaxial screw dislocation. For the coaxial screw dislocation we find a modified formula for the so-called Eshelby twist which depends on a specific intrinsic material length.
Screw dislocations in the field theory of elastoplasticity
Markus Lazar
2002-09-30
A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely long screw dislocation in a cylinder, a dipole of screw dislocations and a coaxial screw dislocation in a finite cylinder. The stress fields have no singularities in the dislocation core and they are modified in the core due to the presence of localized moment stress. Additionally, we calculated the elastoplastic energies for the screw dislocation in a cylinder and the coaxial screw dislocation. For the coaxial screw dislocation we find a modified formula for the so-called Eshelby twist which depends on a specific intrinsic material length.
Real time statistical field theory
M. E. Carrington; T. Fugleberg; D. S. Irvine; D. Pickering
2006-08-28
We have written a {\\it Mathematica} program that calculates the integrand corresponding to any amplitude in the closed-time-path formulation of real time statistical field theory. The program is designed so that it can be used by someone with no previous experience with {\\it Mathematica}. It performs the contractions over the tensor indices that appear in real time statistical field theory and gives the result in the 1-2, Keldysh or RA basis. We have used the program to calculate the ward identity for the QED 3-point function, the QED 4-point function for two photons and two fermions, and the QED 5-point function for three photons and two fermions. In real time statistical field theory, there are seven 3-point functions, 15 4-point functions and 31 5-point functions. We produce a table that gives the results for all of these functions. In addition, we give a simple general expression for the KMS conditions between $n$-point green functions and vertex functions, in both the Keldysh and RA bases
Mean Field Theory for Sigmoid Belief Networks
Saul, Lawrence K.
1996-08-01
We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it ...
Effective Field Theory in Nuclear Physics
Martin J. Savage
2000-07-11
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.
Effective field theory in nuclear physics
Martin J. Savage
2000-12-12
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.
Gravity Duals for Nonrelativistic Conformal Field Theories
McGreevy, John
We attempt to generalize the anti–de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at ...
Motion of small bodies in classical field theory
Gralla, Samuel E. [Enrico Fermi Institute and Department of Physics University of Chicago 5640 S. Ellis Avenue, Chicago, Illinois 60637 (United States)
2010-04-15
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
Symmetries and strings in field theory and gravity
Banks, Tom [School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540 (United States); New High Energy Theory Center, Department of Physics, Rutgers University, Piscataway, New Jersey 08854 (United States); Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, California 95064 (United States); Seiberg, Nathan [School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540 (United States)
2011-04-15
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 Z{sub p} gauge theories shows that they are associated with an emergent Z{sub p} 1-form (Kalb-Ramond) gauge symmetry. This understanding leads us to uncover new observables and new phenomena in nonlinear {sigma} 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.
Nonlocal field theories and their gravity duals
Aaron Bergman; Keshav Dasgupta; Ori J. Ganor; Joanna L. Karczmarek; Govindan Rajesh
2002-01-01
The gravity duals of nonlocal field theories in the large-N limit exhibit a novel behavior near the boundary. To explore this, we present and study the duals of dipole theories, a particular class of nonlocal theories with fundamental dipole fields. The nonlocal interactions are manifest in the metric of the gravity dual, and type-0 string theories make a surprising appearance.
Encoding field theories into gravities
Sinya Aoki; Kengo Kikuchi; Tetsuya Onogi
2015-06-07
We propose a method, which encodes the information of a $d$ dimensional quantum field theory into a $d+1$ dimensional gravity in the $1/N$ expansion. We first construct a $d+1$ dimensional field theory from the $d$ dimensional one via the gradient flow equation, whose flow time $t$ represents the energy scale of the system such that $t\\rightarrow 0$ corresponds to the ultra-violet (UV) while $t\\rightarrow\\infty$ to the infra-red (IR). We then define the induced metric from $d+1$ dimensional field operators. We show that the metric defined in this way becomes classical in the large $N$ limit, in a sense that quantum fluctuations of the metric are suppressed as $1/N$ due to the large $N$ factorization property. As a concrete example, we apply our method to the O(N) non-linear $\\sigma$ model in two dimensions. We calculate the induced metric in three dimensions, which is shown to describe (asymptotically) an AdS space in the massless (UV) limit. We finally discuss several open issues in future studies.
Encoding field theories into gravities
Sinya Aoki; Kengo Kikuchi; Tetsuya Onogi
2015-05-13
We propose a method, which encodes the information of a $d$ dimensional quantum field theory into a $d+1$ dimensional gravity in the $1/N$ expansion. We first construct a $d+1$ dimensional field theory from the $d$ dimensional one via the gradient flow equation, whose flow time $t$ represents the energy scale of the system such that $t\\rightarrow 0$ corresponds to the ultra-violet (UV) while $t\\rightarrow\\infty$ to the infra-red (IR). We then define the induced metric from $d+1$ dimensional field operators. We show that the metric defined in this way becomes classical in the large $N$ limit, in a sense that quantum fluctuations of the metric are suppressed as $1/N$ due to the large $N$ factorization property. As a concrete example, we apply our method to the O(N) non-linear $\\sigma$ model in two dimensions. We calculate the induced metric in three dimensions, which is shown to describe asymptotically De Sitter (dS) or Anti De Sitter (AdS) space in the UV limit. We finally discuss several open issues in future studies.
Noncommutative Dipole Field Theories And Unitarity
Chiou, Dah-Wei; Ganor, Ori J.
2003-10-24
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.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Hamiltonian Anomalies from Extended Field Theories
NASA Astrophysics Data System (ADS)
Monnier, Samuel
2015-05-01
We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.
On conformal field theories with low number of primary fields
Roman Dovgard; Doron Gepner
2009-03-11
Using Verlinde formula and the symmetry of the modular matrix we describe an algorithm to find all conformal field theories with low number of primary fields. We employ the algorithm on up to eight primary fields. Four new conformal field theories are found which do not appear to come from current algebras. This supports evidence to the fact that rational conformal field theories are far richer than suspected before.
Mathematical quantization of Hamiltonian field theories
A. V. Stoyanovsky
2015-02-04
We define the renormalized evolution operator of the Schr\\"odinger equation in the infinite dimensional Weyl-Moyal algebra during a time interval for a wide class of Hamiltonians depending on time. This leads to a mathematical definition of quantum field theory $S$-matrix and Green functions. We show that for renormalizable field theories, our theory yields the renormalized perturbation series of perturbative quantum field theory. All the results are based on the Feynman graph series technique.
Constitutive Theories for Thermoelastic Solids in Lagrangian Description Using Gibbs Potential
Mendoza, Yusshy
2012-08-31
of the constitution of the matter, the second law of thermodynamics, i.e. entropy inequality, must form the basis for all constitutive theories of the deforming matter to ensure thermodynamic equilibrium during the evolution [1, 2]. The entropy inequality expressed...
Permutation Orbifolds in Conformal Field Theories and String Theory
M. Maio
2011-11-03
We summarize the results obtained in the last few years about permutation orbifolds in two-dimensional conformal field theories, their application to string theory and their use in the construction of four-dimensional heterotic string models.
Large N field theories, string theory and gravity
Ofer Aharony; Steven S. Gubser; Juan Maldacena; Hirosi Ooguri; Yaron Oz
2000-01-01
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
Large N Field Theories, String Theory and Gravity
Juan Maldacena; Steven S. Gubser; Hirosi Ooguri; Yaron Oz
1999-01-01
We describe the holographic correspondence between field theories and string\\/M theory, focusing on the relation between compactifications\\u000a of string\\/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence\\u000a and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from\\u000a the correspondence in the regime
Effective Field Theory of Multi-Field Inflation a la Weinberg
Nima Khosravi
2012-03-10
We employ the effective field theory approach for multi-field inflation which is a generalization of Weinberg's work. In this method the first correction terms in addition to standard terms in the Lagrangian have been considered. These terms contain up to the fourth derivative of the fields including the scalar field and the metric. The results show the possible shapes of the interaction terms resulting eventually in non-Gaussianity in a general formalism. In addition generally the speed of sound is different but almost unity. Since in this method the adiabatic mode is not discriminated initially so we define the adiabatic as well as entropy modes for a specific two-field model. It has been shown that the non-Gaussianity of the adiabatic mode and the entropy mode are correlated in shape and amplitude. It is shown that even for speed close to unity large non-Gaussianities are possible in multi-field case. The amount of the non-Gaussianity depends on the curvature of the classical path in the phase-space in the Hubble unit such that it is large for the large curvature. In addition it is emphasized that the time derivative of adiabatic and entropy perturbations do not transform due to the shift symmetry as well as the original perturbations. Though two specific combinations of them are invariant under such a symmetry and these combinations should be employed to construct an effective field theory of multi-field inflation.
Quantum Field Theory in Condensed Matter Physics
Alexei M. Tsvelik
2003-01-01
This course in modern quantum field theory for condensed matter physics includes a derivation of the path integral representation, Feynman diagrams and elements of the theory of metals. Alexei Tsvelik also covers Landau Fermi liquid theory and gradually turns to more advanced methods used in the theory of strongly correlated systems. The book contains a thorough exposition of such non-perturbative
On the theory of a non-linear neutral scalar field with spontaneously broken symmetry
Poluektov, Yu M
2015-01-01
On the example of a real scalar field, an approach to quantization of non-linear fields and construction of the perturbation theory with account of spontaneous symmetry breaking is proposed. The method is based on using as the main approximation of the relativistic self-consistent field model, in which the influence of vacuum fluctuations is taken into account in constructing the one-particle states. The solutions of the self-consistent equations determine possible states, which also include the states with broken symmetries. Different states of the field are matched to particles, whose masses are determined by both parameters of the Lagrangian and vacuum fluctuations.
Energy-momentum currents in Finsler/Kawaguchi Lagrangian formulation
Takayoshi Ootsuka; Ryoko Yahagi; Muneyuki Ishida; Erico Tanaka
2014-07-12
We reformulate the standard Lagrangian formalism to a reparameterisation invariant Lagrangian formalism by means of Finsler and Kawaguchi geometry. In our formalism, various types of symmetries that appears in theories of physics are expressed geometrically by symmetries of Finsler (Kawaguchi) metric, and the conservation law of energy-momentum is a part of Euler-Lagrange equations. The application to scalar field, Dirac field, electromagnetic field and general relativity are discussed. By this formalism, we try to propose an alternative definition of energy-momentum current of gravity.
Noncommutative Tachyons And String Field Theory
Edward Witten
2000-01-01
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
W symmetry in conformal field theory
Peter Bouwknegt; Kareljan Schoutens
1993-01-01
We review various aspects of W algebra symmetry in two-dimensional conformal field theory and string theory. We pay particular attention to the construction of W algebras through the quantum Drinfeld-Sokolov reduction and through the coset construction.
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Supersymmetric field theories and generalized cohomology
NASA Astrophysics Data System (ADS)
Cheung, Pok Man
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.
Effective field theory of multi-field inflation a la Weinberg
NASA Astrophysics Data System (ADS)
Khosravi, Nima
2012-05-01
We generalise Weinberg's effective field theory approach to multiple-field inflation. In addition to standard terms in the Lagrangian we consider terms containing up to the fourth derivative of the scalar fields and the metric. The results illustrate the possible shapes of the interactions which will yield non-Gaussianity. Generally we find that the speed of sound differs from, but is close to unity, however large non-Gaussianities are possible in the multi-field case. The non-Gaussianity of the adiabatic mode and the entropy mode are correlated in shape and amplitude with the amount of the non-Gaussianity depending on the curvature of the classical field path in phase-space. We emphasize that in general the time derivative of adiabatic and entropy perturbations do not invariant due to the shift symmetry. However we find two specific combinations of them are invariant under such a symmetry and these combinations should be employed to construct an effective field theory of multi-field inflation.
Effective field theory calculation of second post-Newtonian binary dynamics
Gilmore, James B.; Ross, Andreas [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States)
2008-12-15
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.
Unitary Fermi Gas, ? Expansion, and Nonrelativistic Conformal Field Theories
NASA Astrophysics Data System (ADS)
Nishida, Yusuke; Son, Dam Thanh
We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the ? expansion technique based on a systematic expansion in terms of the dimensionality of space. We apply this technique to compute the thermodynamic quantities, the quasiparticle cum, and the criticl temperature of UFG. We then discuss consequences of the scale and conformal invariance of UFG. We prove a correspondence between primary operators in nonrelativistic conformal field theories and energy eigenstates in a harmonic potential. We use this correspondence to compute energies of fermions at unitarity in a harmonic potential. The scale and conformal invariance together with the general coordinate invariance constrains the properties of UFG. We show the vanishing bulk viscosities of UFG and derive the low-energy effective Lagrangian for the superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic scaling and conformal symmetries that can be in principle realized in ultracold atom experiments.
Stretched strings in noncommutative field theory
Hong Liu; Jeremy Michelson
2000-01-01
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
Conformal field theory on the plane
Sylvain Ribault
2014-09-19
We provide an introduction to conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry. We describe the mathematical structures which appear in such theories, from the Virasoro algebra and its representations, to the BPZ equations and their solutions. As examples, we study a number of models: Liouville theory, (generalized) minimal models, free bosonic theories, the $H_3^+$ model, and the $SU_2$ and $\\widetilde{SL}_2(\\mathbb{R})$ WZW models.
Euclidean field theory on a sphere
Dirk Schlingemann
1999-12-23
This paper is concerned with a structural analysis of euclidean field theories on the euclidean sphere. In the first section we give proposal for axioms for a euclidean field theory on a sphere in terms of C*-algebras. Then, in the second section, we investigate the short-distance behavior of euclidean field theory models on the sphere by making use of the concept of {\\em scaling algebras}, which has first been introduced by D. Buchholz, and R. Verch and which has also be applied to euclidean field theories on flat euclidean space in a previous paper. We establish the expected statement that that scaling limit theories of euclidean field theories on a sphere are euclidean field theories on flat euclidean space. Keeping in mind that the minkowskian analogue of the euclidean sphere is the de Sitter space, we develop a Osterwalder-Schrader type construction scheme which assigns to a given euclidean field theory on the sphere a quantum field theory on de Sitter space. We show that the constructed quantum field theoretical data fulfills the so called geodesic KMS condition in the sense of H. J. Borchers and D. Buchholz, i.e. for any geodesic observer the system looks like a system within a thermal equilibrium state.
NASA Astrophysics Data System (ADS)
Nucci, M. C.; Leach, P. G. L.
2007-12-01
Searching for a Lagrangian may seem either a trivial endeavor or an impossible task. In this paper, we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H. Goldstein, Classical Mechanics, 2nd edition (Addison-Wesley, Reading, MA, 1980)], and the damped harmonic oscillator. This is the first paper in a series dedicated to this subject.
Soft theorems from effective field theory
NASA Astrophysics Data System (ADS)
Larkoski, Andrew J.; Neill, Duff; Stewart, Iain W.
2015-06-01
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate this explicitly both at tree-level and at one-loop. The effective theory correctly describes these configurations, and we generalize the Low-Burnett-Kroll theorem into a new one-loop subleading soft theorem for amplitudes. Our analysis is presented in a manner that illustrates the wider utility of using effective theory techniques to understand the perturbative S-matrix.
Hamiltonian Vector Fields on Multiphase Spaces of Classical Field Theory
Michael Forger; Mário Otávio Salles
2010-10-02
We present a classification of hamiltonian vector fields on multisymplectic and polysymplectic fiber bundles closely analogous to the one known for the corresponding dual jet bundles that appear in the multisymplectic and polysymplectic approach to first order classical field theories.
General Gauge Field Theory And Its Application
Ning Wu
1998-07-19
A gauge field model, which simultaneously has strict local gauge symmetry and contains massive general gauge bosons, is discussed in this paper. The model has SU(N) gauge symmetry. In order to introduce the mass term of gauge fields directly without violating the gauge symmetry of the theory, two sets of gauge fields will be introduced into the theory. After some transformations, one set of gauge fields obtain masses and another set of gauge fields keep massless. In the limit $\\alpha \\longrightarrow 0$ or $\\alpha \\longrightarrow \\infty$, the gauge field model discussed in this paper will return to Yang-Mills gauge field model. Finally, some applications of this model are discussed.
NASA Astrophysics Data System (ADS)
Moayedi, S. K.; Setare, M. R.; Khosropour, B.
2013-11-01
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; Khosropour, B
2013-01-01
In the 1990s, Kempf and his collaborators Mangano and Mann introduced a $D$-dimensional $(\\beta,\\beta')$-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length $(\\triangle X^{i})_{min}=\\hbar\\sqrt{D\\beta+\\beta'}\\;,\\forall i\\in \\{1,2, \\cdots,D\\}$. 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 $\\beta'=2\\beta$ up to the first order over $\\beta$. 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 conc...
S. K. Moayedi; M. R. Setare; B. Khosropour
2013-10-15
In the 1990s, Kempf and his collaborators Mangano and Mann introduced a $D$-dimensional $(\\beta,\\beta')$-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length $(\\triangle X^{i})_{min}=\\hbar\\sqrt{D\\beta+\\beta'}\\;,\\forall i\\in \\{1,2, \\cdots,D\\}$. 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 $\\beta'=2\\beta$ up to the first order over $\\beta$. 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 $4.42\\times10^{-19}m$. The relationship between magnetostatics with a minimal length and the Gaete-Spallucci non-local magnetostatics (J. Phys. A: Math. Theor. \\textbf{45}, 065401 (2012)) is investigated.
Renormalization and Stability in Semiclassical Field Theories
Barrett Rogers
1991-01-01
Working in the functional Schrodinger picture formalism, a prescription is given to define a class of quantum states of a scalar field which are renormalizable in the context of semiclassical field theories. This prescription is then used in the study of two physical systems. The first consists of a weak, uniform electric field coupled to a charged, scalar matter field.
String field theory vertex from integrability
Bajnok, Zoltan
2015-01-01
We propose a framework for computing the (light cone) string field theory vertex in the case when the string worldsheet QFT is a generic integrable theory. The prime example and ultimate goal would be the $AdS_5 \\times S^5$ superstring theory cubic string vertex and the chief application will be to use this framework as a formulation for ${ \\cal N}=4$ SYM theory OPE coefficients valid at any coupling up to wrapping corrections. In this paper we propose integrability axioms for the vertex, illustrate them on the example of the pp-wave string field theory and also uncover similar structures in weak coupling computations of OPE coefficients.
Pairwise interaction method in crystal field theory
R. B. Dushin; L. D. Shcherba
1985-01-01
We describe a new variant of crystal field theory — the pairwise interaction method. The pairwise interaction method is a superposition variant of crystal field theory in which as the parameters we use the shifts in the one-electron orbital energy levels of the innerZ-electron under the action of the perturbation caused by a single ligand. We establish a relationship between
Pairwise interaction method in crystal field theory
R. B. Dushin; L. D. Shcherba
1986-01-01
The authors describe a new variant of crystal field theory - the pairwise interaction method. The pairwise interaction method is a superposition variant of crystal field theory in which as the parameters they use the shifts in the one-electron orbital energy levels of the inner Z-electron under the action of the perturbation caused by a single ligand. They establish a
Three approaches to classical thermal field theory
NASA Astrophysics Data System (ADS)
Gozzi, E.; Penco, R.
2011-04-01
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.
String Field Theory Around the Tachyon Vacuum
Leonardo Rastelli; Ashoke Sen; Barton Zwiebach
2000-01-01
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
Euclidean quantum field theory: Curved spacetimes and gauge fields
William Gordon Ritter
2007-01-01
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
Gauge Theory Wilson Loops and Conformal Toda Field Theory
Filippo Passerini
2010-03-15
The partition function of a family of four dimensional N=2 gauge theories has been recently related to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory is A_1 conformal Toda field theory, i.e. Liouville theory. For this case the relation has been extended showing that the expectation value of gauge theory loop operators can be reproduced in Liouville theory inserting in the correlators the monodromy of chiral degenerate fields. In this paper we study Wilson loops in SU(N) gauge theories in the fundamental and anti-fundamental representation of the gauge group and show that they are associated to monodromies of a certain chiral degenerate operator of A_{N-1} Toda field theory. The orientation of the curve along which the monodromy is evaluated selects between fundamental and anti-fundamental representation. The analysis is performed using properties of the monodromy group of the generalized hypergeometric equation, the differential equation satisfied by a class of four point functions relevant for our computation.
Killing Vector Fields and Superharmonic Field Theories
Josua Groeger
2013-01-23
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, referred to as superharmonic action, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of the superharmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
LanHEP - a package for the automatic generation of Feynman rules in field theory. Version 3.0
A. Semenov
2008-05-05
The LanHEP program version 3.0 for Feynman rules generation from the Lagrangian is described. It reads the Lagrangian written in a compact form, close to the one used in publications. It means that Lagrangian terms can be written with summation over indices of broken symmetries and using special symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Supersymmetric theories can be described using the superpotential formalism and the 2-component fermion notation. The output is Feynman rules in terms of physical fields and independent parameters in the form of CompHEP model files, which allows one to start calculations of processes in the new physical model. Alternatively, Feynman rules can be generated in FeynArts format or as LaTeX table. One-loop counterterms can be generated in FeynArts format.
Mean-field theory and ? expansion for Anderson localization
NASA Astrophysics Data System (ADS)
Harris, A. B.; Lubensky, T. C.
1981-03-01
A general field-theoretic formulation of the Anderson model for the localization of wave functions in a random potential is given in terms of n-component replicated fields in the limit n-->0, and is analyzed primarily for spatial dimension d>=4. Lengths ?1 and ?2 associated with the spatial decay of correlations in the single-particle and two-particle Green's functions, respectively, are introduced. Two different regimes, the weak coupling and strong coupling, are distinguished depending on whether ?-11 or ?-12, respectively, vanishes as the mobility energy, Ec, is approached. The weak-coupling regime vanishes as d-->4+. Mean-field theory is developed from the uniform minimum of the Lagrangian for both the strong- and weak-coupling cases. For the strong-coupling case it gives the exponents va=14, ?a=?a=12, ?=0, and ?=1, where ?a is the exponent associated with the density of extended states and ? is that associated with the conductivity. Simple heuristic arguments are used to verify the correctness of these unusual mean-field values. Infrared divergences in perturbation theory for the strong-coupling case occur for d<8, and an ? expansion (?=8-d) is developed which is found to be identical to that previously analyzed for the statistics of lattice animals and which gives ?a=12-?12, ?=-?9, va=14+?36, and ?=1-5?36. The results are consistent with the Ward identity, which in combination with scaling arguments requires that ?a+?a=1. The treatment takes account of the fact that the average of the on-site Green's function [G(x-->,x-->E)]av is nonzero and is predicated on this quantity being real, i.e., on the density of states vanishing at the mobility edge. We also show that localized states emerge naturally from local minima of finite action in the Lagrangian. These instanton solutions are analyzed on a lattice where the cutoff produced by the lattice constant leads to lattice instantons which exist for all d, in contrast to the case for the continuum model where instanton solutions seem not to occur for d>4. This analysis leads to a density of localized states ?loc satisfying ln?loc~-E2 at large E and ln?loc~-|E-Ec|-? at the mobility edge, where for the weak-coupling case ?=(12)(d-4) and for the strong-coupling case ?=(d-2+?)va-2?a=12+?18 for d<8 and ?=(14)(d-6) for d>8. A brief discussion of the relationship between this work and the theories of localization below four dimensions is presented.
Space–time noncommutative field theories and unitarity
Jaume Gomis; Thomas Mehen
2000-01-01
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
The facets of relativistic quantum field theory
H. G. Dosch; V. F. Müller
2011-01-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with\\u000a the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form\\u000a is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short
Descent relations in cubic superstring field theory
NASA Astrophysics Data System (ADS)
Aref'eva, I. Y.; Gorbachev, R.; Medvedev, P. B.; Rychkov, D. V.
2008-01-01
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.
General properties of noncommutative field theories
Miguel A. Vazquez-Mozo
In this paper we study general properties of noncommutative field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. We analyze the extension of the Wightman axioms to this context and explore their consequences, in particular we present a proof of the CPT theorem for theories with space-space noncommu- tativity. We analyze as
Green functions in stochastic field theory
NASA Astrophysics Data System (ADS)
Honkonen, Juha
2013-03-01
Functional representations are reviewed for the generating function of Green functions of stochastic problems stated either with the use of the Fokker-Planck equation or the master equation. Both cases are treated in a unified manner based on the operator approach similar to quantum mechanics. Solution of a second-order stochastic differential equation in the framework of stochastic field theory is constructed. Ambiguities in the mathematical formulation of stochastic field theory are discussed. The Schwinger-Keldysh representation is constructed for the Green functions of the stochastic field theory which yields a functional-integral representation with local action but without the explicit functional Jacobi determinant or ghost fields.
Holographic description of quantum field theory
Sung-Sik Lee
2010-01-01
We propose that general D-dimensional quantum field theories are dual to (D+1)-dimensional local quantum theories which in general include objects with spin two or higher. Using a general prescription, we construct a (D+1)-dimensional theory which is holographically dual to the D-dimensional O(N) vector model. From the holographic theory, the phase transition and critical properties of the model in dimensions D>2
Geometric Engineering of Quantum Field Theories
Sheldon Katz; Albrecht Klemm; Cumrun Vafa
1996-01-01
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
Unified field theories and Einstein
S C Tiwari
2006-02-16
Einstein's contribution to relativity is reviewed. It is pointed out that Weyl gave first unified theory of gravitation and electromagnetism and it was different than the five dimensional theory of Kaluza. Einstein began his work on unification in 1925 that continued whole through the rest of his life.
Scalar fields in the nonsymmetric Kaluza-Klein (Jordan-Thiry) theory
M. W. Kalinowski
2015-07-07
In this paper we construct the Nonsymmetric Jordan-Thiry Theory unifying N.G.T., the Yang-Mills' field, the Higgs' fields and scalar forces in a geometric manner. In this way we get masses from higher dimensions. We discuss spontaneous symmetry breaking, the Higgs' mechanism and a mass generation in the theory. The scalar field (as in the classical Jordan-Thiry Theory) is connected to the effective gravitational constant. This field is massive and has Yukawa-type behaviour. We derive the equation of motion for a test particle from conservation laws in the hydrodynamic limit. We consider a truncation procedure for a tower of massive scalar fields using Friedrichs' theory and an approximation procedure for the lagrangian involving Higgs' field. The geodetic equations on the Jordan-Thiry manifold are considered with an emphasis to terms involving Higgs' field. We consider also field equations in linear approximation. We consider a dynamics of Higgs' field in the framework of cosmological models involving the scalar field. The scalar field plays here a role of a quintessence field. We consider phase transition in cosmological models of the second and the first order. We consider a warp factor known from some modern approaches. We consider a toy model of a time-machine. We consider a mass of a quintessence particle, various properties of a quintessence field. We calculate a speed of sound in a quintessence and fluctuations of a quintessence caused by primordial metric fluctuations.
BPS solitons in Lifshitz field theories
Kobakhidze, Archil; Thompson, Jayne E.; Volkas, Raymond R. [School of Physics, University of Melbourne, Victoria 3010 (Australia)
2011-01-15
Lorentz-invariant scalar-field theories in d+1 dimensions with second-order derivative terms are unable to support static soliton solutions that are both finite in energy and stable for d>2, a result known as Derrick's theorem. Lifshitz theories, which introduce higher-order spatial derivatives, need not obey Derrick's theorem. We construct stable, finite-energy, static soliton solutions in Lifshitz scalar-field theories in 3+1 dimensions with a dynamical critical exponent z=2. We exhibit three generic types: nontopological point defects, topological point defects, and topological strings. We focus mainly on Lifshitz theories that are defined through a superpotential and admit Bogomolnyi-Prasad-Sommerfield solutions. These kinds of theories are the bosonic sectors of supersymmetric theories derived from the stochastic dynamics of a scalar field theory in one higher dimension. If nature obeys a Lifshitz field theory in the ultraviolet, then the novel topological defects discussed here may exist as relics from the early universe. Their discovery would prove that standard field theory breaks down at short distance scales.
Supergeometry in locally covariant quantum field theory
Hack, Thomas-Paul; Schenkel, Alexander
2015-01-01
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc --> S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the en...
Cosmological implications of conformal field theory
Nesbet, R K
2009-01-01
Requiring all elementary fields to have conformal scaling symmetry removes a formal conflict between Einstein-Hilbert gravitational theory and the quantum theory of elementary particles and fields. Higgs symmetry-breaking requires a nonvanishing scalar field throughout spacetime, a cosmological entity. In uniform, isotropic geometry, conformal gravitational theory that includes this scalar field determines a modified Friedmann evolution equation with nonvanishing cosmological constant. Numerical solution determines parameters consistent with empirical data for redshifts $z\\leq z_*=1090$, including luminosity distances for observed type Ia supernovae and peak structure ratios in the cosmic microwave background (CMB). In this theory, a cosmological constant within current empirical error bounds implies extremely small mass for the Higgs boson. A simplified but internally consistent model of nucleosynthesis determines baryon number density from the empirical CMB temperature and acoustic wave velocity. The theory...
Valuation theory of exponential Hardy fields
Kuhlmann, Franz-Viktor
2012-01-01
We describe the residue fields of arbitrary convex valuations on certain o-minimal expansions of the ordered field of real numbers. References: [1] Franz-Viktor and Salma Kuhlmann: Residue fields of arbitrary convex valuations on restricted analytic fields with exponentiation I, The Fields Institute Preprint Series (1997). [2] Franz-Viktor and Salma Kuhlmann: Valuation theory of exponential Hardy fields I, Mathematische Zeitschrift 243, 671--688 (2003) [3] Ordered Exponential Fields, by Salma Kuhlmann, The Fields Institute Monograph Series Vol. 12, (2000).
Generating functionals and Lagrangian partial differential equations
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
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.
Effective field theory out of equilibrium: Brownian quantum fields
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2015-06-01
The emergence of an effective field theory out of equilibrium is studied in the case in which a light field—the system—interacts with very heavy fields in a finite temperature bath. We obtain the reduced density matrix for the light field, its time evolution is determined by an effective action that includes the influence action from correlations of the heavy degrees of freedom. The non-equilibrium effective field theory yields a Langevin equation of motion for the light field in terms of dissipative and noise kernels that obey a generalized fluctuation dissipation relation. These are completely determined by the spectral density of the bath which is analyzed in detail for several cases. At T = 0 we elucidate the effect of thresholds in the renormalization aspects and the asymptotic emergence of a local effective field theory with unitary time evolution. At T\
Recent Progress of Crystal Field Theory
Satoru Sugano
1962-01-01
A brief account is given concerning the theoretical framework of the molecular orbital treatment of crystal field theory. Indirect and direct experimental evidences of electron delocalization are summarized. A historical survey is given of the theoretical treatment of cubic crystal field splitting. Finally, a molecular orbital treatment of the cubic field splitting is presented, emphasizing the importance of ?-electron bonding
Effective Field Theory of Multi-Field Inflation a la Weinberg
Khosravi, Nima
2012-01-01
We employ the effective field theory approach for multi-field inflation which is a generalization of Weinberg's work. In this method the first correction terms in addition to standard terms in the Lagrangian have been considered. These terms contain up to the fourth derivative of the fields including the scalar field and the metric. The results show the possible shapes of the interaction terms resulting eventually in non-Gaussianity in a general formalism. In addition generally the speed of sound is different but almost unity. Since in this method the adiabatic mode is not discriminated initially so we define the adiabatic as well as entropy modes for a specific two-field model. It has been shown that the non-Gaussianity of the adiabatic mode and the entropy mode are correlated in shape and amplitude. It is shown that even for speed close to unity large non-Gaussianities are possible in multi-field case. The amount of the non-Gaussianity depends on the curvature of the classical path in the phase-space in the...
Time independent mean-field theory
Negele, J.W.
1980-02-01
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.
Overlaps in pilot wave field theories
I. Schmelzer
2009-12-05
Recently doubts have been raised about the ability of pilot wave theories with field ontology to recover the predictions of quantum field theory. In particular, Struyve has questioned that the overlap between wave functionals of macroscopically different states with fixed particle number is really non-significant. With numerical computations and some further plausibility arguments we show that the overlap between n-particle states in field theory decreases almost exponentially with the number of particles and becomes non-significant already for small particle numbers.
Stochastic modeling of Lagrangian accelerations
NASA Astrophysics Data System (ADS)
Reynolds, Andy
2002-11-01
It is shown how Sawford's second-order Lagrangian stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.
Discrete Pluriharmonic Functions as Solutions of Linear Pluri-Lagrangian Systems
NASA Astrophysics Data System (ADS)
Bobenko, A. I.; Suris, Yu. B.
2015-05-01
Pluri-Lagrangian systems are variational systems with the multi-dimensional consistency property. This notion has its roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics, in the theory of variational symmetries going back to Noether and in the theory of discrete integrable systems. A d-dimensional pluri-Lagrangian problem can be described as follows: given a d-form L on an m-dimensional space, m > d, whose coefficients depend on a function u of m independent variables (called field), find those fields u which deliver critical points to the action functionals for any d-dimensional manifold ? in the m-dimensional space. We investigate discrete 2-dimensional linear pluri-Lagrangian systems, i.e., those with quadratic Lagrangians L. The action is a discrete analogue of the Dirichlet energy, and solutions are called discrete pluriharmonic functions. We classify linear pluri-Lagrangian systems with Lagrangians depending on diagonals. They are described by generalizations of the star-triangle map. Examples of more general quadratic Lagrangians are also considered.
A Superdimensional Dual-covariant Approach to Unified Field Theory
Yaroslav Derbenev
2014-08-01
An approach to a Unified Field Theory (UFT) is developed as an attempt to establish unification of the Theory of Quantum Fields (QFT) and General Theory of Relativity (GTR) on the background of a covariant differential calculus. A dual State Vector field (DSV)consisting of covariant and contravariant N-component functions of variables of a N-dimensional unified manifod (UM)is introduced to represents matter. DSV is supposed to transform in a way distinct from that of the differentials of the UM variables. Consequently, the hybrid tensors and a hybrid affine tensor (Dynamic Connection, DC) are introduced. The hybrid curvature form (HCF) is introduced as a covariant derivative of DC. A system of covariant Euler-Lagrange (EL) equations for DSV, DC, and a twin couple of the triadic hybrid tensors (Split Metric, SM)is derived. A scalar Lagrangian form is composed based on a set of principles suited for UFT, including the homogeneity in the UM space, differential irreducibility and scale invariance. The type of the manifold geometry is not specified in advance, in neither local (signature) nor regional (topology) aspects. Equations for DSV play role of the Schroedinger-Dirac equation in space of UM. By the correspondent EL equations, DC and SM are connected to DSV and become responsible for the non-linear features of the system i.e. interactions. In this paper we mark breaking of a background paradigm of the modern QFT, the superposition principle. The issue of the UM-MF dimensionality will be addressed, and relations to the principles and methodology of QFT and GTR will be discussed.
Radiation reaction and gravitational waves in the effective field theory approach
Chad R. Galley; Manuel Tiglio
2009-03-05
We compute the contribution to the Lagrangian from the leading order (2.5 post-Newtonian) radiation reaction and the quadrupolar gravitational waves emitted from a binary system using the effective field theory (EFT) approach of Goldberger and Rothstein. We use an initial value formulation of the underlying (quantum) framework to implement retarded boundary conditions and describe these real-time dissipative processes. We also demonstrate why the usual scattering formalism of quantum field theory inadequately accounts for these. The methods discussed here should be useful for deriving real-time quantities (including radiation reaction forces and gravitational wave emission) and hereditary terms in the post-Newtonian approximation (including memory, tail and other causal, history-dependent integrals) within the EFT approach. We also provide a consistent formulation of the radiation sector in the equivalent effective field theory approach of Kol and Smolkin.
Orbits in Space: Lagrangian points
NSDL National Science Digital Library
Stern, David P. (David Peter), 1931-
Authored and curated by David P. Stern, these pages explore orbits and the "Lagrangian points", where objects will orbit the sun with the same period as the earth. This has applications for solar monitoring spacecraft. The three sections derive the equilibrium properties of Lagrangian points: the calculations only involve algebra and trig, but are rather lengthy. This is a nice introduction to these rather complex theories of orbits in space. Translations to French and (in part) Spanish are also provided.
Effective field theories for inclusive B decays
Lee, Keith S. M. (Keith Seng Mun)
2006-01-01
In this thesis, we study inclusive decays of the B meson. These allow one to determine CKM elements precisely and to search for physics beyond the Standard Model. We use the framework of effective field theories, in ...
Quantum field theories on the Lefschetz thimble
M. Cristoforetti; F. Di Renzo; A. Mukherjee; L. Scorzato
2013-12-04
In these proceedings, we summarize the Lefschetz thimble approach to the sign problem of Quantum Field Theories. In particular, we review its motivations, and we summarize the results of the application of two different algorithms to two test models.
Conformal field theory of twisted vertex operators
NASA Astrophysics Data System (ADS)
Dolan, L.; Goddard, P.; Montague, P.
1990-07-01
The Z2-twisted bosonic conformal field theory associated with a d-dimensional momentum lattice ? 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, ? is even, and ?2? ? is also even. (This last condition is weaker than self-duality for ?, a further requirement which may be necessary for the theory to be defined on higher-genus surfaces.) The construction and properties of cocycle operators are described. Locality implies the closure of the operator product expansion, and thus that all the weight-one fields are guaranteed to close to form an affine algebra. Applications are to the construction of the natural module of Frenkel et al. for the Monster group, and to an improved understanding of twist fields in relation to gauge algebras in string theory.
Effective Field Theory for Nuclear Physics
David B. Kaplan
1999-01-01
I summarize the motivation for the effective field theory approach to nuclear physics, and highlight some of its recent accomplishments. The results are compared with those computed in potential models.
Effective Field Theory in Condensed Matter Physics
R. Shankar
1997-01-01
Some personal reminiscences are followed by a brief illustration of how effective field theories are used in condensed matter physics. Examples include Landau's Fermi liquid, sigma models with topological terms, Dirac fermions and the Gross Neveu model.
Quantum Field Theory of Fluids
Gripaios, Ben; Sutherland, Dave
2015-02-18
would need to somehow ensure that ther- mal fluctuations are negligible in the long-distance fluid modes, which are what we quantize here. Alternatively, perhaps the correspondence of the theory with a fluid at the classical level is a red herring. We...
An Extremal N=2 Superconformal Field Theory
Nathan Benjamin; Ethan Dyer; A. Liam Fitzpatrick; Shamit Kachru
2015-06-30
We provide an example of an extremal chiral ${\\cal N}=2$ superconformal field theory at $c=24$. The construction is based on a ${\\mathbb Z}_2$ orbifold of the theory associated to the $A_{1}^{24}$ Niemeier lattice. The statespace is governed by representations of the sporadic group $M_{23}$.
Geometric continuum regularization of quantum field theory
Halpern, M.B. (California Univ., Berkeley, CA (USA). Dept. of Physics)
1989-11-08
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.
Lagrangian reduction and the double spherical pendulum
Jerrold E. Marsden; Juergen Scheurle
1993-01-01
This paper studies the stability and bifurcations of the relative equilibrium of the double spherical pendulum, which has the circle as its symmetry group. The example as well as others with nonabelian symmetry groups, such as the rigid body, illustrate some useful general theory about Lagrangian reduction. In particular, we establish a satisfactory global theory of Lagrangian reduction that is
Simple Recursion Relations for General Field Theories
Clifford Cheung; Chia-Hsien Shen; Jaroslav Trnka
2015-05-20
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.
Asymptotic states and renormalization in Lorentz-violating quantum field theory
Mauro Cambiaso; Ralf Lehnert; Robertus Potting
2014-09-09
Asymptotic single-particle states in quantum field theories with small departures from Lorentz symmetry are investigated perturbatively with focus on potential phenomenological ramifications. To this end, one-loop radiative corrections for a sample Lorentz-violating Lagrangian contained in the Standard-Model Extension (SME) are studied at linear order in Lorentz breakdown. It is found that the spinor kinetic operator, and thus the free-particle physics, is modified by Lorentz-violating operators absent from the original Lagrangian. As a consequence of this result, both the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism need to be adapted. The necessary adaptations are worked out explicitly at first order in Lorentz-breaking coefficients.
Currents and the energy-momentum tensor in classical field theory: a fresh look at an old problem
NASA Astrophysics Data System (ADS)
Forger, Michael; Römer, Hartmann
2004-02-01
We give a comprehensive review of various methods to define currents and the energy-momentum tensor in classical field theory, with emphasis on a geometric point of view. The necessity of "improving" the expressions provided by the canonical Noether procedure is addressed and given an adequate geometric framework. The main new ingredient is the explicit formulation of a principle of "ultralocality" with respect to the symmetry generators, which is shown to fix the ambiguity inherent in the procedure of improvement and guide it towards a unique answer: when combined with the appropriate splitting of the fields into sectors, it leads to the well-known expressions for the current as the variational derivative of the matter field Lagrangian with respect to the gauge field and for the energy-momentum tensor as the variational derivative of the matter field Lagrangian with respect to the metric tensor. In the second case, the procedure is shown to work even when the matter field Lagrangian depends explicitly on the curvature, thus establishing the correct relation between scale invariance, in the form of local Weyl invariance "on shell", and tracelessness of the energy-momentum tensor, required for a consistent definition of the concept of a conformal field theory.
Luca Pinter
1999-01-01
This theory proposes a way to achieve super-photonic speed for space travel with our present superconducting and superfluid technology with low energy's consumption. The relativistic mass increase is avoided by using a complete transformation of heat-thermal energy into a work-dynamical one. This could be permitted from the theoretical explanation of the local ondulatory nature of inertia and using physical conditions
8.324 Relativistic Quantum Field Theory II, Fall 2005
Zwiebach, Barton
This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth ...
Superstring field theory in the democratic picture
Michael Kroyter
2010-11-04
We present a new open superstring field theory, whose string fields carry an arbitrary picture number and reside in the large Hilbert space. The redundancy related to picture number is resolved by treating picture changing as a gauge transformation. A mid-point insertion is imperative for this formalism. We find that this mid-point insertion must include all multi-picture changing operators. It is also proven that this insertion as well as all the multi-picture changing operators are zero weight conformal primaries. This new theory solves the problems with the Ramond sector shared by other RNS string field theories, while naturally unifying the NS and Ramond string fields. When partially gauge fixed, it reduces in the NS sector to the modified cubic superstring field theory. Hence, it shares all the good properties of this theory, e.g., it has analytical vacuum and marginal deformation solutions. Treating the redundant gauge symmetry using the BV formalism is straightforward and results in a cubic action with a single string field, whose quantum numbers are unconstrained. The generalization to an arbitrary brane system is simple and includes the standard Chan-Paton factors and the most general string field consistent with the brane system.
Power counting in nuclear effective field theory
NASA Astrophysics Data System (ADS)
Valderrama, M. Pavon
2015-10-01
The effective field theory formulation of nuclear forces is able to provide a systematic and model independent description of nuclear physics, where all processes involving nucleons and pions can be described in terms of the same set of couplings, the theoretical errors are known in advance and the connection with QCD is present. These features are a consequence of renormalization group invariance, which in turn determines the power counting of the theory. Here we present a brief outline of how to determine the power counting of nuclear effective field theory, what does it looks like and what are the predictions for the two-nucleon sector at lowest orders.
Neutron beta decay in effective field theory
S. Ando; H. W. Fearing; V. Gudkov; K. Kubodera; F. Myhrer; S. Nakamura; T. Sato
2004-06-03
Radiative corrections to the lifetime and angular correlation coefficients of neutron beta-decay are evaluated in effecitive field theory. We also evaluate the lowest order nucleon recoil corrections, including weak-magnetism. Our results agree with those of the long-range and model-independent part of previous calculations. In an effective theory the model-dependent radiative corrections are replaced by well-defined low-energy constants. The effective field theory allows a systematic evaluation of higher order corrections to our results to the extent that the relevant low-energy constants are known.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (?(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. PMID:22654052
Teleparallelism-A viable theory of gravity?
Folkert Müller-Hoissen; Jürgen Nitsch
1983-01-01
The teleparallelism theory of gravity is presented as a constrained Poincaré gauge theory. Arguments are given in favor of a two-parameter family of field Lagrangians quadratic in torsion. The inclusion of a \\
Intertwiners in orbifold conformal field theories
NASA Astrophysics Data System (ADS)
Montague, P. S.
1997-02-01
Following on from earlier work relating modules of meromorphic bosonic conformal field theories to states representing solutions of certain simple equations inside the theories, we show, in the context of orbifold theories, that the intertwiners between twisted sectors are unique and described explicitly in terms of the states corresponding to the relevant modules. No explicit knowledge of the structure of the twisted sectors is required. Further, we propose a general set of sufficiency conditions, illustrated in the context of a third-order no-fixed-point twist of a lattice theory, for verifying consistency of arbitrary orbifold models in terms of the states representing the twisted sectors.
Viscosity, Black Holes, and Quantum Field Theory
D. T. Son; A. O. Starinets
2007-07-11
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 quasinormal modes of the AdS black p-brane metric. We provide a 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.
Closure procedures in crystal field theory
J. Killingbeck
1970-01-01
The group symmetry and unitary invariance of certain projection operators are discussed, and it is pointed out that closure approximations impose particular group symmetries on the intermediate states projection operators of second-order perturbation theory. The unitary invariance property of projection operators enables evaluation of second-order crystal field effects for a term without detailed knowledge of the crystal field levels of
Some theoretical investigations in crystal field theory
O. L. Malta
1979-01-01
General expressions for the crystal field parameters are established by the introduction of an electronic charge density which depends on the operator Ô(n) = |?n >< ?n|, where |?n> is an eigenstate of the system (central ion + ligands). The connection with molecular orbital theory is discussed as well as the expected behaviour of the crystal field parameters with the
Some theoretical investigations in crystal field theory
O. L. Malta
1979-01-01
General expressions for the crystal field parameters are established by the introduction of an electronic charge density which depends on the operator Ô(n) = |psin > is an eigenstate of the system (central ion + ligands). The connection with molecular orbital theory is discussed as well as the expected behaviour of the crystal field parameters with the eigenstates |psin> for
The Boltzmann Equation in Scalar Field Theory
NASA Astrophysics Data System (ADS)
Brandt, F. T.; Frenkel, J.; Guerra, A.
We derive the classical transport equation, in scalar field theory with a g2V(?) interaction, from the equation of motion for the quantum field. We obtain a very simple, but iterative, expression for the effective action ? which generates all the n-point Green functions in the high-temperature limit. An explicit and closed form is given for ? in the static case.
Information Spreading in Interacting String Field Theory
D. A. Lowe; L. Susskind; J. Uglum
1994-02-24
The commutator of string fields is considered in the context of light cone string field theory. It is shown that the commutator is in general non--vanishing outside the string light cone. This could have profound implications for our understanding of the localization of information in quantum gravity.
D-branes and string field theory
Sigalov, Ilya
2006-01-01
In this thesis we study the D-brane physics in the context of Witten's cubic string field theory. We compute first few terms the low energy effective action for the non-abelian gauge field A, from Witten's action. We show ...
Quantum Field Theory Mark Srednicki
Akhmedov, Azer
;5 41 LSZ Reduction for Spin-One-Half Particles (5, 39) 263 42 The Free Fermion Propagator (39) 268 43 The Path Integral for Fermion Fields (9, 42) 272 44 Formal Development of Fermionic Path Integrals (43) 276 of the Electron (63) 383 65 Loop Corrections in Scalar Electrodynamics (61, 62) 386 66 Beta Functions in Quantum
Conformal field theory on affine Lie groups
Clubok, K.S.
1996-04-01
Working directly on affine Lie groups, we construct several new formulations of the WZW model, the gauged WZW model, and the generic affine-Virasoro action. In one formulation each of these conformal field theories (CFTs) is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation each CFT is written as a two-dimensional field theory, with a three- dimensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translation dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional formulations on the Lie group. Using this dictionary, we also express each CFT as a three-dimensional field theory on the Lie group with a four-dimensional WZW term. 36 refs.
Singular Perturbations in Quantum Field Theory
V. E. Rochev; P. A. Saponov
1995-10-30
In this talk we discuss a new approximation scheme for non-perturbative calculations in a quantum field theory which is based on the fact that the Schwinger equation of a quantum field model belongs to the class of singularly perturbed equations. The self-interacting scalar field and the Gross-Neveu model are taken as the examples and some non-perturbative solutions of an equation for the propagator are found for these models. The application to QCD is also discussed.
Propagation of field disturbances in Yang-Mills theory
De Lorenci, Vitorio A.; Li Shiyuan [Institute of Science, Federal University of Itajuba, 37500-903 Itajuba, M. G. (Brazil); PH Department, TH Unit, CERN, 1211 Geneva 23 (Switzerland); School of Physics, Shandong University, Jinan, 250100 (China); PH Department, TH Unit, CERN, 1211 Geneva 23 (Switzerland)
2008-08-01
The propagation of field disturbances is examined in the context of the effective Yang-Mills Lagrangian, which is intended to be applied to QCD systems. It is shown that birefringence phenomena can occur in such systems provided some restrictive conditions, as causality, are fulfilled. Possible applications to phenomenology are addressed.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
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.
Theory of cosmological seed magnetic fields
Saleem, H. [Theoretical Plasma Physics Division (TPPD), PINSTECH, P. O. Nilore, Islamabad (Pakistan)
2007-07-15
A theory for the generation of seed magnetic field and plasma flow on cosmological scales driven by externally given baroclinic vectors is presented. The Beltrami-like plasma fields can grow from zero values at initial time t=0 from a nonequilibrium state. Exact analytical solutions of the set of two-fluid equations are obtained that are valid for large plasma {beta}-values as well. Weaknesses of previous models for seed magnetic field generation are also pointed out. The analytical calculations predict the galactic seed magnetic field generated by this mechanism to be of the order of 10{sup -14} G, which may be amplified later by the {alpha}{omega} dynamo (or by some other mechanism) to the present observed values of the order of {approx}(2-10) {mu}G. The theory has been applied to laser-induced plasmas as well and the estimate of the magnetic field's magnitude is in agreement with the experimentally observed values.
The role of the Beltrami parametrization of complex structures in 2-d Free Conformal Field Theory
Serge Lazzarini
2005-09-30
This talk gives a review on how complex geometry and a Lagrangian formulation of 2-d conformal field theory are deeply related. In particular, how the use of the Beltrami parametrization of complex structures on a compact Riemann surface fits perfectly with the celebrated locality principle of field theory, the latter requiring the use infinite dimensional spaces. It also allows a direct application of the local index theorem for families of elliptic operators due to J.-M. Bismut, H. Gillet and C. Soul\\'{e}. The link between determinant line bundles equipped with the Quillen\\'s metric and the so-called holomorphic factorization property will be addressed in the case of free spin $j$ b-c systems or more generally of free fields with values sections of a holomorphic vector bundles over a compact Riemann surface.
Simple Recursion Relations for General Field Theories
Cheung, Clifford; Trnka, Jaroslav
2015-01-01
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-...
Geometry of 2D topological field theories
Boris Dubrovin
1994-01-01
These lecture notes are devoted to the theory of equations of associativity\\u000adescribing geometry of moduli spaces of 2D topological field theories.\\u000aIntroduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.}\\u000aPolynomial solutions of WDVV. {Appendix B.} Symmetriies of WDVV. Twisted\\u000aFrobenius manifolds. {Appendix C.} WDVV and Chazy equation. Affine connections\\u000aon curves with projective structure. Lecture 2. Topological
Selected Issues in Thermal Field Theory
Chihiro Sasaki
2014-08-04
New developments on hot and dense QCD in effective field theories are reviewed. Recent investigations in lattice gauge theories for the low-lying Dirac eigenmodes suggest survival hadrons in restored phase of chiral symmetry. We discuss expected properties of those bound states in a medium using chiral approaches. The role of higher-lying hadrons near chiral symmetry restoration is also argued from the conventional and the holographic point of view.
Quantum field theory of treasury bonds
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2001-07-01
The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.
Renormalization of a model quantum field theory
Kraus, P.; Griffiths, D.J. (Physics Department, Reed College, Portland, Oregon 97202 (United States))
1992-11-01
Renormalization is the technique used to eliminate infinities that arise in quantum field theory. This paper shows how to renormalize a particularly simple model, in which a single mass counterterm of second order in the coupling constant suffices to cancel all divergences. The model serves as an accessible introduction to Feynman diagrams, covariant perturbation theory, and dimensional regularization, as well as the renormalization procedure itself.
Neutrix Calculus and Finite Quantum Field Theory
Y. Jack Ng; H. van Dam
2005-04-04
In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT,obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework.
Tachyon condensation in string field theory
Ashoke Sen; Barton Zwiebach
2000-01-01
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
Topological field theory and rational curves
Paul S. Aspinwall; David R. Morrison
1993-01-01
We analyze the quantum field theory corresponding to a string propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear ?-model and the structure of rational curves on the Calabi-Yau manifold. We study in detail the case of the world-sheet of the string being mapped to a multiple cover of an isolated rational curve
Dual PT-Symmetric Quantum Field Theories
Bender, C M; Rivers, R J
2005-01-01
Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a $\\gamma_5$ mass term the Hamiltonian is $\\cal PT$-symmetric. Depending on the mass parameter this symmetry may be either broken or unbroken. When the $\\cal PT$ symmetry is unbroken, the spectrum of the quantum field theory is real. For the $\\cal PT$-symmetric version of the massive Thirring model in two-dimensional space-time, which is dual to the $\\cal PT$-symmetric scalar Sine-Gordon model, an exact construction of the $\\cal C$ operator is given. It is shown that the $\\cal PT$-symmetric massive Thirring and Sine-Gordon models are equivalent to the conventional Hermitian massive Thirring and Sine-Gordon models with appropriately shifted masses.
Nonequilibrium statistical field theory for classical particles: Basic kinetic theory
NASA Astrophysics Data System (ADS)
Viermann, Celia; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2015-06-01
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010), 10.1103/PhysRevE.81.061102; J. Stat. Phys. 149, 643 (2012), 10.1007/s10955-012-0610-y; J. Stat. Phys. 152, 159 (2013), 10.1007/s10955-013-0755-3; Phys. Rev. E 83, 041125 (2011), 10.1103/PhysRevE.83.041125] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
Ligand Field Theory: An ever-modern theory
NASA Astrophysics Data System (ADS)
Daul, Claude A.
2013-04-01
The Ligand Field (LF) model in molecular science or the Crystal Field model in condensed matter science has been introduced more than eighty years ago. Since then, this theory plays a central role each time that molecules containing d- and/or f-elements with open shells are adressed. No doubt, this fact is related to the dominant localisation of the frontier orbitals within the metal-sphere. This common feature enables us to describe approximately the electronic structure of these molecules using orbitals that are centred on a single atom and to treat their interaction with the chemical environment essentially as a perturbation. Another reason for the success of this simple theory is the fact that the more accurate molecular orbital theory does generally over-estimate covalence of transition metal atoms and thus yields wave functions that are too delocalized. We give here a survey of the development of LF theory since its introduction simultaneously by Hans Bethe and John Hasbrouck van Vleck more than eighty years ago. Over the years, LF theory was a semi-empirical model with adjustable parameter until the end of last century when we introduced non-empirical LF theory that is based on DFT calculations. The results of this first-principle prediction are in very good agreement with the experimental observations. Sample calculations of tetrahedral and octahedral Cr-complexes and hexa-acquo Ni(II)-complexes are used to validate the new model and to analyse the calculated parameters
Quantum field theory based on birefringent modified Maxwell theory
M. Schreck
2014-09-04
In the current paper the properties of a birefringent Lorentz-violating extension of quantum electrodynamics is considered. The theory results from coupling modified Maxwell theory, which is a CPT-even Lorentz-violating extension of the photon sector, to a Dirac theory of standard spin-1/2 particles. It is then restricted to a special birefringent case with one nonzero Lorentz-violating coefficient. The modified dispersion laws of electromagnetic waves are obtained plus their phase and group velocities are considered. After deriving the photon propagator and the polarization vectors for a special momentum configuration we prove both unitarity at tree-level and microcausality for the quantum field theory based on this Lorentz-violating modification. These analytical proofs are done for a spatial momentum with two vanishing components and the proof of unitarity is supported by numerical investigations in case all components are nonvanishing. The upshot is that the theory is well-behaved within the framework of our assumptions where there is a possible issue for negative Lorentz-violating coefficients. The paper shall provide a basis for the future analysis of alternative birefringent quantum field theories.
Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators
Landon Lehman
2014-12-26
We present a complete list of the independent dimension-7 operators that are constructed using the Standard Model degrees of freedom and are invariant under the Standard Model gauge group. This list contains only 20 independent operators; far fewer than the 63 operators available at dimension 6. All of these dimension-7 operators contain fermions and violate lepton number, and 7 of the 20 violate baryon number as well. This result extends the Standard Model Effective Field Theory (SMEFT) and allows a more detailed exploration of the structure and properties of possible deformations from the Standard Model Lagrangian.
Non-exponential decay in Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Giacosa, Francesco
2014-10-01
We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.
On the theory of a non-linear neutral scalar field with spontaneously broken symmetry
Y. M. Poluektov
2015-07-08
On the example of a real scalar field, an approach to quantization of non-linear fields and construction of the perturbation theory with account of spontaneous symmetry breaking is proposed. The method is based on using as the main approximation of the relativistic self-consistent field model, in which the influence of vacuum field fluctuations is taken into account when constructing the one-particle states. The solutions of the self-consistent equations determine possible states, which also include the states with broken symmetries. Different states of the field are matched to particles, whose masses are determined by both parameters of the Lagrangian and vacuum fluctuations. The density of the vacuum energy in these states is calculated. It is shown that the concept of Bogolubov's quasi-averages can naturally be applied for definition of exact Green functions in the states with broken symmetries. Equations for exact one- and two-point Green functions are obtained.
Supergeometry in locally covariant quantum field theory
Thomas-Paul Hack; Florian Hanisch; Alexander Schenkel
2015-01-07
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc --> S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1|1-dimensions and the free Wess-Zumino model in 3|2-dimensions.
Holographic Duals of 4D Field Theories
M. Porrati; A. Starinets
2000-09-25
We discuss various aspect of the holographic correspondence between 5-d gravity and 4-d field theory. First of all, we describe deformations of N=4 Super Yang-Mills (SYM) theories in terms of 5-d gauged supergravity. In particular, we describe N=0 and N=1 deformations of N=4 SYM to confining theories. Secondly, we describe recent proposals for the holographic dual of the renormalization group and for 4-d central charges associated to it. We conclude with a ``holographic'' proof of the Goldstone theorem.
Experimental Bounds on Classical Random Field Theories
NASA Astrophysics Data System (ADS)
Peters, Joffrey K.; Fan, Jingyun; Migdall, Alan L.; Polyakov, Sergey V.
2015-07-01
Alternative theories to quantum mechanics motivate important fundamental tests of our understanding and descriptions of the smallest physical systems. Here, using spontaneous parametric downconversion as a heralded single-photon source, we place experimental limits on a class of alternative theories, consisting of classical field theories which result in power-dependent normalized correlation functions. In addition, we compare our results with standard quantum mechanical interpretations of our spontaneous parametric downconversion source over an order of magnitude in intensity. Our data match the quantum mechanical expectations, and do not show a statistically significant dependence on power, limiting quantum mechanics alternatives which require power-dependent autocorrelation functions.
Holographic Gauge Theory with Maxwell Magnetic Field
Wung-Hong Huang
2009-01-01
We first apply the transformation of mixing azimuthal with wrapped coordinate\\u000ato the 11D M-theory with a stack N M5-branes to find the spacetime of a stack\\u000aof N D4-branes with magnetic field in 10D IIA string theory, after the\\u000aKaluza-Klein reduction. In the near-horizon limit the background becomes the\\u000aMelvin magnetic field deformed $AdS_6 \\\\times S^4$. Although the solution
Conformal Field Theory and black hole physics
NASA Astrophysics Data System (ADS)
Sidhu, Steve
2012-01-01
This thesis reviews the use of 2-dimensional conformal field theory applied to gravity, specifically calculating Bekenstein-Hawking entropy of black holes in (2+1) dimensions. A brief review of general relativity, Conformal Field Theory, energy extraction from black holes, and black hole thermodynamics will be given. The Cardy formula, which calculates the entropy of a black hole from the AdS/CFT duality, will be shown to calculate the correct Bekenstein-Hawking entropy of the static and rotating BTZ black holes. The first law of black hole thermodynamics of the static, rotating, and charged-rotating BTZ black holes will be verified.
On the theory of gravitation field
N. N. Chaus
1999-03-12
We construct a general relativity formula for the law of gravity for material bodies. The formula contains three numeric parameters that are to be determined experimentally. If they are chosen from symmetry considerations, then the theory that appears is close to the theory of electrodynamics: the gravitational field is given by two vector fields, one can write the energy-momentum tensor, we give an answer on the question what a gravitational wave is. Going to infinity, this wave carries with it the negative energy.
Unified Field Theory of Four Interactions Tian Ma, Shouhong Wang
Wang, Shouhong
Unified Field Theory of Four Interactions Tian Ma, Shouhong Wang Supported in part by NSF, ONR and Chinese NSF http://www.indiana.edu/~fluid I. Two Roads to a Unified Field Theory II. Unified Field Theory. Two Roads to a Unified Field Theory Four fundamental forces/interactions in Nature: 2 #12;1. Einstein
Coherent states formulation of polymer field theory
Man, Xingkun; Villet, Michael C. [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States) [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States); Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States); Delaney, Kris T. [Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States)] [Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States); Orland, Henri [Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex (France)] [Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex (France); Fredrickson, Glenn H., E-mail: ghf@mrl.ucsb.edu [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States); Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States); Materials Department, University of California, Santa Barbara, California 93106 (United States)
2014-01-14
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.
Astrophysical data analysis with information field theory
NASA Astrophysics Data System (ADS)
Enßlin, Torsten
2014-12-01
Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), 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. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
Scalar Quantum Field Theory on Fractals
Arnab Kar; S. G. Rajeev
2011-10-02
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale invariant scalar field theories, by imitating Wiener's construction of the measure on the space of functions of one variable. These are Gaussian measures, except for one example of a non-Gaussian fixed point for the Ising model on a fractal. In the continuum limits what we construct have correlation functions that vary as a power of distance. In most cases this is a positive power (as for the Wiener measure) but we also find a few examples with negative exponent. In all cases the exponent is an irrational number, which depends on the particular subdivision scheme used. This suggests that the continuum limits corresponds to quantum field theories (random fields) on spaces of fractional dimension.
Scalar Quantum Field Theory on Fractals
Kar, Arnab
2011-01-01
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale invariant scalar field theories, by imitating Wiener's construction of the measure on the space of functions of one variable. These are Gaussian measures, except for one example of a non-Gaussian fixed point for the Ising model on a fractal. In the continuum limits what we construct have correlation functions that vary as a power of distance. In most cases this is a positive power (as for the Wiener measure) but we also find a few examples with negative exponent. In all cases the exponent is an irrational number, which depends on the particular subdivision scheme used. This suggests that the continuum limits corresponds to quantum field theories (random fields) on spaces of fractional dimension.
Configuration Interaction in Crystal Field Theory
K. Rajnak; B. G. Wybourne
1964-01-01
The effect of configuration interaction on the validity of the usual method of expanding the crystal field potential in terms of spherical harmonics is examined using second-order perturbation theory. It is found that for a configuration of equivalent electrons lN most mechanisms of configuration interaction lead to a simple scaling of the crystal field parameters Bqk. However, one-electron excitations, either
On Higher Spatial Derivative Field Theories
Pedro R. S. Gomes; M. Gomes
2012-04-23
In this work, we employ renormalization group methods to study the general behavior of field theories possessing anisotropic scaling in the spacetime variables. The Lorentz breaking symmetry that accompanies these models are either soft, if no higher spatial derivative is present, or it may have a more complex structure if higher spatial derivatives are also included. Both situations are discussed in models with only scalar fields and also in models with fermions as a Yukawa like model.
The MSW Effect in Quantum Field Theory
Christian Y. Cardall; Daniel J. H. Chung
1999-04-12
We show in detail the general relationship between the Schr\\"{o}dinger equation approach to calculating the MSW effect and the quantum field theoretical S-matrix approach. We show the precise form a generic neutrino propagator must have to allow a physically meaningful ``oscillation probability'' to be decoupled from neutrino production fluxes and detection cross-sections, and explicitly list the conditions---not realized in cases of current experimental interest---in which the field theory approach would be useful.
Quantum field theory and gravity in causal sets
NASA Astrophysics Data System (ADS)
Sverdlov, Roman M.
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.
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
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.
Continuous Wavelet Transform in Quantum Field Theory
Altaisky, Mikhail V
2013-01-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar $\\phi^4$ theory, quantum electrodynamics, quantum chromodynamics. The method of continuous wavelet transform in quantum field theory presented in M.Altaisky Phys. Rev. D81(2010)125003 for the scalar $\\phi^4$ theory, consists in substitution of the local fields $\\phi(x)$ by those dependent on both the position $x$ and the resolution $a$. The substitution of the action $S[\\phi(x)]$ by the action $S[\\phi_a(x)]$ makes the local theory into nonlocal one, and implies the causality conditions related to the scale $a$, the region causality C. Christensen and L. Crane, J.Math. Phys 46 (2005) 122502. These conditions make the Green functions $G(x_1,a_1,..., x_n,a_n)= $ finite for any given set of regions by means of an effective cutoff scale $A=\\min (a_1,...,a_n)$.
Continuous Wavelet Transform in Quantum Field Theory
Mikhail V. Altaisky; Natalia E. Kaputkina
2013-07-13
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar $\\phi^4$ theory, quantum electrodynamics, quantum chromodynamics. The method of continuous wavelet transform in quantum field theory presented in M.Altaisky Phys. Rev. D81(2010)125003 for the scalar $\\phi^4$ theory, consists in substitution of the local fields $\\phi(x)$ by those dependent on both the position $x$ and the resolution $a$. The substitution of the action $S[\\phi(x)]$ by the action $S[\\phi_a(x)]$ makes the local theory into nonlocal one, and implies the causality conditions related to the scale $a$, the region causality J.D. Christensen and L. Crane, J.Math. Phys 46 (2005) 122502. These conditions make the Green functions $G(x_1,a_1,..., x_n,a_n)= $ finite for any given set of regions by means of an effective cutoff scale $A=\\min (a_1,...,a_n)$.
Modelling a Particle Detector in Field Theory
Fabio Costa; Federico Piazza
2009-11-04
Particle detector models allow to give an operational definition to the particle content of a given quantum state of a field theory. The commonly adopted Unruh-DeWitt type of detector is known to undergo temporary transitions to excited states even when at rest and in the Minkowski vacuum. We argue that real detectors do not feature this property, as the configuration "detector in its ground state + vacuum of the field" is generally a stable bound state of the underlying fundamental theory (e.g. the ground state-hydrogen atom in a suitable QED with electrons and protons) in the non-accelerated case. As a concrete example, we study a local relativistic field theory where a stable particle can capture a light quantum and form a quasi-stable state. As expected, to such a stable particle correspond energy eigenstates of the full theory, as is shown explicitly by using a dressed particle formalism at first order in perturbation theory. We derive an effective model of detector (at rest) where the stable particle and the quasi-stable configurations correspond to the two internal levels, "ground" and "excited", of the detector.
Global effects in quaternionic quantum field theory
S. P. Brumby; G. C. Joshi
1996-10-07
We present some striking global consequences of a model quaternionic quantum field theory which is locally complex. We show how making the quaternionic structure a dynamical quantity naturally leads to the prediction of cosmic strings and non-baryonic hot dark matter candidates.
Global effects in quaternionic quantum field theory
Brumby, S P
1996-01-01
We present some striking global consequences of a model quaternionic quantum field theory which is locally complex. We show how making the quaternionic structure a dynamical quantity naturally leads to the prediction of cosmic strings and non-baryonic hot dark matter candidates.
Gauged supergravity and holographic field theory
Nick Warner
2003-01-01
This is a slightly expanded version of my talk at Future Perspectives in Theoretical Physics and Cosmology, Stephen Hawking's 60th Birthday Worshop. I describe some of the issues that were important in gauged supergravity in the 1980's and how these, and related issues have once again become important in the study of holographic field theories.
Dirac-Kaehler Theory and Massless Fields
Pletyukhov, V. A. [Kosmonavtov av. 21, Brest, 224016 BELARUS (Belarus); Strazhev, V. I. [Nezavisimosti av. 4, Minsk, 220030 (Belarus)
2010-03-24
Three massless limits of the Dirac-Kaehler theory are considered. It is shown that the Dirac-Kaehler equation for massive particles can be represented as a result of the gauge-invariant mixture (topological interaction) of the above massless fields.
Mineralogical Applications of Crystal Field Theory
Roger G. Burns
1993-01-01
The new edition of this landmark volume takes into account the vast amount of new spectral data on minerals, and describes a variety of applications of crystal field theory to the earth and planetary sciences. A unique perspective of the second edition is that it highlights the properties of minerals that make them compounds of interest to solid state chemists
Mineralogical Applications of Crystal Field Theory
Roger G. Burns
2005-01-01
The new edition of this landmark volume takes into account the vast amount of new spectral data on minerals, and describes a variety of applications of crystal field theory to the earth and planetary sciences. A unique perspective of the second edition is that it highlights the properties of minerals that make them compounds of interest to solid state chemists
Crystal Field Theory in the Rare Earths
R. J. Elliott
1953-01-01
The paramagnetic properties (in particular the resonance data) of the rare earth ethyl sulfates are considered in the light of a theory in which each ion is assumed to be in a static electric field of C3h symmetry. It is found that this is consistent with the observations in cerium ethyl sulfate, and it is possible to solve that problem
Modular bootstrap in Liouville field theory
Leszek Hadasz; Zbigniew Jaskolski; Paulina Suchanek
2009-11-22
The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.
Topological Interpretations of Lattice Gauge Field Theory
Doug Bullock; Charles Frohman; Joanna Kania-Bartoszynska
1998-01-01
We construct lattice gauge field theory based on a quantum group on a lattice of dimension one. Innovations include a coalgebra structure on the connections and an investigation of connections that are not distinguishable by observables. We prove that when the quantum group is a deformation of a connected algebraic group G (over the complex numbers), then the algebra of
Cross Sections From Scalar Field Theory
NASA Technical Reports Server (NTRS)
Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel
2008-01-01
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.
Closed string field theory from polyhedra
Maha Saadi; Barton Zwiebach
1989-01-01
A fully nonpolynomial framework for closed string field theory is studied. All interactions are geometrical, the pattern of string overlaps gives polyhedra with equal perimeter faces and three edges at each vertex. All interactions are cubic in the sense that at most three strings can coincide at a point. The three point vertex used is that of Witten which is
Analogue gravity from field theory normal modes?
Carlos Barceló; Stefano Liberati; Matt Visser
2001-01-01
We demonstrate that the emergence of a curved spacetime `effective Lorentzian geometry' is a common and generic result of linearizing a classical scalar field theory around some non-trivial background configuration. This investigation is motivated by considering the large number of `analogue models' of general relativity that have recently been developed based on condensed matter physics, and asking whether there is
de Sitter entropy from conformal field theory
Daniel Kabat; Gilad Lifschytz
2002-01-01
We propose that the entropy of de Sitter space can be identified with the mutual entropy of a dual conformal field theory. We argue that unitary time evolution in de Sitter space restricts the total number of excited degrees of freedom to be bounded by the de Sitter entropy, and we give a CFT interpretation of this restriction. We also
The quantum symmetry of rational field theories
NASA Astrophysics Data System (ADS)
Fuchs, Jürgen
1994-03-01
The quantum symmetry of a rational quantum field theory is a finite-dimensional multi-matrix algebra. Its representation category, which determines the fusion rules and braid group representations of superselection sectors, is a braided monoidal C*-category. Various properties of such algebraic structures are described, and some ideas concerning the classification programme are outlined.
Weighting bubbles in group field theory
NASA Astrophysics Data System (ADS)
Baratin, Aristide; Freidel, Laurent; Gurau, Razvan
2014-07-01
Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the bubbles of the graphs in the Feynman evaluations. In dimension three, our model exhibits new symmetries, interpreted as the action of the vertex translations of the triangulation. The extra field indices have an elegant algebraic interpretation: they encode the structure of a semisimple algebra. Remarkably, when the algebra is chosen to be associative, the new structure contributes a topological invariant from each bubble of the graph to the Feynman amplitudes.
Relating Field Theories via Stochastic Quantization
Robbert Dijkgraaf; Domenico Orlando; Susanne Reffert
2009-05-03
This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the quantization method used to obtain the quantum crystal is a discrete analog of stochastic quantization. This model is of interest for string theory, since the (classical) melting crystal corner is related to the topological A-model. We outline several ideas for interpreting the quantum crystal on the string theory side of the correspondence, exploring interpretations in the Wheeler-De Witt framework and in terms of a non-Lorentz invariant limit of topological M-theory.
Symmetry aspects of nonholonomic field theories
J. Vankerschaver; D. Martin de Diego
2007-12-14
The developments in this paper are concerned with nonholonomic field theories in the presence of symmetries. Having previously treated the case of vertical symmetries, we now deal with the case where the symmetry action can also have a horizontal component. As a first step in this direction, we derive a new and convenient form of the field equations of a nonholonomic field theory. Nonholonomic symmetries are then introduced as symmetry generators whose virtual work is zero along the constraint submanifold, and we show that for every such symmetry, there exists a so-called momentum equation, describing the evolution of the associated component of the momentum map. Keeping up with the underlying geometric philosophy, a small modification of the derivation of the momentum lemma allows us to treat also generalized nonholonomic symmetries, which are vector fields along a projection. Such symmetries arise for example in practical examples of nonholonomic field theories such as the Cosserat rod, for which we recover both energy conservation (a previously known result), as well as a modified conservation law associated with spatial translations.
Sigma Models as Perturbed Conformal Field Theories
Fendley, Paul
1999-11-29
We show that two-dimensional sigma models are related to certain perturbed conformal field theories. When the fields in the sigma model take values in a space G/H for a group G and a maximal subgroup H , we argue that the corresponding conformal field theory is the k{yields}{infinity} limit of the coset model (G/H){sub k} , and the perturbation is related to the current of G . Nonperturbative instanton contributions to the sigma model free energy are perturbative when k is finite. We use this mapping to find the free energy for the ''O(n) '' [=O(n)/O(n-1) ] sigma model at nonzero temperature. It also results in a new approach to the CP{sup n} model. (c) 1999 The American Physical Society.
Extending Gurwitsch's field theory of consciousness.
Yoshimi, Jeff; Vinson, David W
2015-07-01
Aron Gurwitsch's theory of the structure and dynamics of consciousness has much to offer contemporary theorizing about consciousness and its basis in the embodied brain. On Gurwitsch's account, as we develop it, the field of consciousness has a variable sized focus or "theme" of attention surrounded by a structured periphery of inattentional contents. As the field evolves, its contents change their status, sometimes smoothly, sometimes abruptly. Inner thoughts, a sense of one's body, and the physical environment are dominant field contents. These ideas can be linked with (and help unify) contemporary theories about the neural correlates of consciousness, inattention, the small world structure of the brain, meta-stable dynamics, embodied cognition, and predictive coding in the brain. PMID:25916764
The 't Hooft interaction at finite T and $?$: Beyond the mean field theory
Yasuo Umino; Vicente Vento
2000-12-06
We use the N-quantum approach (NQA) to quantum field theory to construct a solution of the two flavor effective instanton induced `t Hooft interaction model valid for any temperature (T) and chemical potential ($\\mu$) beyond the mean field theory. The model contains only the $\\bar{q}q$ channels. In constructing this solution we calculate the masses, widths and coupling constants of bound $\\sigma$ and resonant color $\\bar{3}$ scalar diquark states. We find that the chemical potential induced by the interaction cancel exactly for all values of T in contrast to the Nambu-Jona-Lasinio model. Our method can also be extended to include the qq channels in the model Lagrangian and we discuss how the NQA can be used to study the properties of bound diquark states at finite T and $\\mu$.
Effective Lagrangians and low energy photon-photon scattering
Duane A. Dicus; Chung Kao; Wayne W. Repko
1998-01-31
We use the behavior of the photon-photon scattering for photon energies $\\omega$ less than the electron mass, $m_e$, to examine the implications of treating the Euler-Heisenberg Lagrangian as an effective field theory. Specifically, we determine the $\\omega^2/m_e^2$ behavior of the scattering amplitude predicted by including one-loop corrections to the Euler-Heisenberg effective Lagrangian together with the counterterms required by renomalizability. This behavior is compared with the energy dependence obtained by expanding the exact QED photon-photon scattering amplitude. If the introduction of counterterms in the effective field theory is restricted to those determined by renormalizability, the $\\omega^2/m_e^2$ dependences of the two expansions differ.
Saririan, K.
1997-05-01
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.
Conservation laws. Generation of physical fields. Principles of field theories
L. I. Petrova
2007-04-19
In the paper the role of conservation laws in evolutionary processes, which proceed in material systems (in material media) and lead to generation of physical fields, is shown using skew-symmetric differential forms. In present paper the skew-symmetric differential forms on deforming (nondifferentiable) manifolds were used in addition to exterior forms, which have differentiable manifolds as a basis. Such skew-symmetric forms (which were named evolutionary ones since they possess evolutionary properties), as well as the closed exterior forms, describe the conservation laws. But in contrast to exterior forms, which describe conservation laws for physical fields, the evolutionary forms correspond to conservation laws for material systems. The evolutionary forms possess an unique peculiarity, namely, the closed exterior forms are obtained from these forms. It is just this that enables one to describe the process of generation of physical fields, to disclose connection between physical fields and material systems and to resolve many problems of existing field theories.
Inflation and deformation of conformal field theory
Garriga, Jaume; Urakawa, Yuko, E-mail: jaume.garriga@ub.edu, E-mail: yurakawa@ffn.ub.es [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona (Spain)
2013-07-01
It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation ? and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.
Comments on double field theory and diffeomorphisms
Jeong-Hyuck Park
2013-06-08
As the theory is subject to a section condition, coordinates in double field theory do not represent physical points in an injective manner. We argue that a physical point should be rather one-to-one identified with a `gauge orbit' in the coordinate space. The diffeomorphism symmetry then implies an invariance under arbitrary reparametrizations of the gauge orbits. Within this generalized sense of diffeomorphism, we show that a recently proposed tensorial transformation rule for finite coordinate transformations is actually (i) consistent with the standard exponential map, and further (ii) compatible with the full covariance of the `semi-covariant' derivatives and curvatures after projectors are properly imposed.
Remarks on twisted noncommutative quantum field theory
Zahn, Jochen [II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
2006-05-15
We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature.
Dirac quantization of parametrized field theory
NASA Astrophysics Data System (ADS)
Varadarajan, Madhavan
2007-02-01
Parametrized field theory (PFT) is free field theory on flat spacetime in a diffeomorphism invariant disguise. It describes field evolution on arbitrary (and in general, curved) foliations of the flat spacetime instead of only the usual flat foliations, by treating the “embedding variables” which describe the foliation as dynamical variables to be varied in the action in addition to the scalar field. A formal Dirac quantization turns the constraints of PFT into functional Schrödinger equations which describe evolution of quantum states from an arbitrary Cauchy slice to an infinitesimally nearby one. This formal Schrödinger picture-based quantization is unitarily equivalent to the standard Heisenberg picture-based Fock quantization of the free scalar field if scalar field evolution along arbitrary foliations is unitarily implemented on the Fock space. Torre and Varadarajan (TV) showed that for generic foliations emanating from a flat initial slice in spacetimes of dimension greater than 2, evolution is not unitarily implemented, thus implying an obstruction to Dirac quantization. We construct a Dirac quantization of PFT, unitarily equivalent to the standard Fock quantization, using techniques from loop quantum gravity (LQG) which are powerful enough to supercede the no-go implications of the TV results. The key features of our quantization include an LQG type representation for the embedding variables, embedding-dependent Fock spaces for the scalar field, an anomaly free representation of (a generalization of) the finite transformations generated by the constraints, and group averaging techniques. The difference between the 1+1-dimensional case and the case of higher spacetime dimensions is that for the latter, only finite gauge transformations are defined in quantum theory, not the infinitesimal ones.
The Vacuum in Light Front Field Theory
NASA Astrophysics Data System (ADS)
Herrmann, Marc; Polyzou, Wayne
2015-04-01
In the light-front formulation of quantum field theory, one finds that the interacting vacuum and the free-field vacuum are both the same trivial Fock vacuum. This stands in contrast to the more usual equal time formulation, where the interacting vacuum and the free vacuum have a complicated relationship. To examine this apparent inconsistency, we first focus on free-fields with two distinct masses. The characterization of the vacuum by annihilation operators is incomplete, and leads to an apparent contradiction concerning the creation and annihilation operators of the two theories. Alternatively, the vacuum can be considered as a positive linear functional on an operator algebra generated by the field. In this characterization, the definition of the vacuum depends on the choice of algebra. The physically relevant algebra should be Poincare invariant and contain local observables. Extending the light-front algebra to this local algebra provides a resolution to the apparent inconsistency, but allows one to still use the Fock vacuum. These results can then be applied to interacting theories. This work supported by DOE Contract No. DE-FG02-86ER40286
Conformal field theories in a periodic potential: Results from holography and field theory
Chesler, Paul
We study (2+1)-dimensional conformal field theories (CFTs) with a globally conserved U(1) charge, placed in a chemical potential which is periodically modulated along the spatial direction x with zero average: ?(x)=V?cos(kx). ...
Lagrangian continuum dynamics in ALEGRA.
Wong, Michael K. W.; Love, Edward
2007-12-01
Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.
M. M. Sharma; A. R. Farhan; G. Münzenberg
2005-01-01
We have investigated properties of $\\\\alpha$-decay chains of recently produced\\u000asuperheavy elements Z=115 and Z=113 using the new Lagrangian model NL-SV1 with\\u000ainclusion of the vector self-coupling of $\\\\omega$ meson in the framework of the\\u000arelativistic mean-field theory. It is shown that the experimentally observed\\u000aalpha-decay energies and half-lives are reproduced well by this Lagrangian\\u000amodel. Further calculations for the
Graphene as a Lattice Field Theory
Simon Hands; Wes Armour; Costas Strouthos
2015-01-08
We introduce effective field theories for the electronic properties of graphene in terms of relativistic fermions propagating in 2+1 dimensions, and outline how strong inter-electron interactions may be modelled by numerical simulation of a lattice field theory. For strong enough coupling an insulating state can form via condensation of particle-hole pairs, and it is demonstrated that this is a theoretical possibility for monolayer graphene. For bilayer graphene the effect of an interlayer bias voltage can be modelled by the introduction of a chemical potential (akin to isopsin chemical potential in QCD) with no accompanying sign problem; simulations reveal the presence of strong interactions among the residual degrees of freedom at the resulting Fermi surface, which is disrupted by an excitonic condensate. We also present preliminary results for the quasiparticle dispersion, which permit direct estimates of both the Fermi momentum and the induced gap.
Operator algebra in logarithmic conformal field theory
Nagi, Jasbir
2005-10-15
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the extensions of this machinery to the logarithmic case are studied and used. More precisely, from Moebius symmetry constraints, the generic three- and four-point functions of logarithmic quasiprimary fields are calculated in closed form for arbitrary Jordan rank. As an example, c=0 disordered systems with nondegenerate vacua are studied. With the aid of two-, three-, and four-point functions, the operator algebra is obtained and associativity of the algebra studied.
Gravity duals for nonrelativistic conformal field theories.
Balasubramanian, Koushik; McGreevy, John
2008-08-01
We attempt to generalize the anti-de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and, more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with a negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and find two-point correlators of the correct form. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions. PMID:18764448
Unstable-particle effective field theory
M. Beneke
2015-01-29
Unstable particles are notorious in perturbative quantum field theory for producing singular propagators in scattering amplitudes that require regularization by the finite width. In this review I discuss the construction of an effective field theory for unstable particles, based on the hierarchy of scales between the mass, M, and the width,Gamma, of the unstable particle that allows resonant processes to be systematically expanded in powers of the coupling alpha and Gamma/M, thereby providing gauge-invariant approximations at every order. I illustrate the method with the next-to-leading order line-shape of a scalar resonance in an abelian gauge-Yukawa model, and results on NLO and dominant NNLO corrections to (resonant and non-resonant) pair production of W-bosons and top quarks.
Why are tensor field theories asymptotically free?
Rivasseau, Vincent
2015-01-01
In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a $1/p^2$ propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex whereas in the vector case, the lack of asymptotic freedom ("Landau ghost"), as in the ordinary scalar case, is simply due to the absence of any wave function renormalization at one loop.
Noisy Lagrangian Tracers for Filtering Random Rotating Compressible Flows
NASA Astrophysics Data System (ADS)
Chen, Nan; Majda, Andrew J.; Tong, Xin T.
2015-06-01
The recovery of a random turbulent velocity field using Lagrangian tracers that move with the fluid flow is a practically important problem. This paper studies the filtering skill of -noisy Lagrangian tracers in recovering random rotating compressible flows that are a linear combination of random incompressible geostrophically balanced (GB) flow and random rotating compressible gravity waves. The idealized random fields are defined through forced damped random amplitudes of Fourier eigenmodes of the rotating shallow-water equations with the rotation rate measured by the Rossby number . In many realistic geophysical flows, there is fast rotation so satisfies and the random rotating shallow-water equations become a slow-fast system where often the primary practical objective is the recovery of the GB component from the Lagrangian tracer observations. Unfortunately, the -noisy Lagrangian tracer observations are highly nonlinear and mix the slow GB modes and the fast gravity modes. Despite this inherent nonlinearity, it is shown here that there are closed analytical formulas for the optimal filter for recovering these random rotating compressible flows for any involving Ricatti equations with random coefficients. The performance of the optimal filter is compared and contrasted through mathematical theorems and concise numerical experiments with the performance of the optimal filter for the incompressible GB random flow with -noisy Lagrangian tracers involving only the GB part of the flow. In addition, a sub-optimal filter is defined for recovering the GB flow alone through observing the -noisy random compressible Lagrangian trajectories, so the effect of the gravity wave dynamics is unresolved but effects the tracer observations. Rigorous theorems proved below through suitable stochastic fast-wave averaging techniques and explicit formulas rigorously demonstrate that all these filters have comparable skill in recovering the slow GB flow in the limit for any bounded time interval. Concise numerical experiments confirm the mathematical theory and elucidate various new features of filter performance as the Rossby number , the number of tracers and the tracer noise variance change.
Gauged Supergravity and Holographic Field Theory
Nicholas P. Warner
2002-01-01
This is a slightly expanded version of my talk at Future Perspectives in\\u000aTheoretical Physics and Cosmology, Stephen Hawking's 60th Birthday Worshop. I\\u000adescribe some of the issues that were important in gauged supergravity in the\\u000a1980's and how these, and related issues have once again become important in\\u000athe study of holographic field theories.
Some boundary effects in quantum field theory
Bezerra, V.B.; Rego-Monteiro, M.A. [Departamento de Fisica, Universidade Federal da Paraiba, Caixa Postal 5008, 58051-970 Joao Pessoa, PB (Brazil); Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ (Brazil)
2004-09-15
We have constructed a quantum field theory in a finite box, with periodic boundary conditions, using the hypothesis that particles living in a finite box are created and/or annihilated by the creation and/or annihilation operators, respectively, of a quantum harmonic oscillator on a circle. An expression for the effective coupling constant is obtained, showing explicitly its dependence on the dimension of the box.
The Global Approach to Quantum Field Theory
S A Fulling
2006-01-01
Bryce Seligman DeWitt (1923–2004), a friend and mentor to many, was a towering figure in the development of the quantum theories of gravity and gauge fields. To appreciate his uniqueness, one must recall the history through which he lived. From DeWitt's birth date through 1965, general relativity (GR) was considered to have so few empirically testable predictions that its practitioners
Field theory in condensed matter physics
CARLOS A. A. DE
Field theory, born as a description of high energy physics, is also used at much lower energies, in condensed matter physics and statistical mechanics. \\\\Ve make a historical survey oC haw this usage cvolvcd, fram the Dirac equation to the presento RESU~tEN. La teoría de campo, inicialmente utilizada en la física de altas energías, se usa también a mucho más
The propagator in polymer quantum field theory
Golam Mortuza Hossain; Viqar Husain; Sanjeev S. Seahra
2011-03-23
We study free scalar field theory on flat spacetime using a background independent (polymer) quantization procedure. Specifically we compute the propagator using a method that takes the energy spectrum and position matrix elements of the harmonic oscillator as inputs. We obtain closed form results in the infrared and ultraviolet regimes that give Lorentz invariance violating dispersion relations, and show suppression of propagation at sufficiently high energy.
A grand superspace for unified field theories
Arthur E. Fischer
1986-01-01
Agrand superspace is proposed as the phase space for gauge field theories with a fixed structure groupG over a fixed space-time manifoldM. This superspace incorporatesall principal fiber bundles with these data. This phase space is the space of isomorphism classes ofall connections onall G-principal fiber bundles overM (fixedG andM). The justification for choosing this grand superspace for the phase space
A new multisymplectic unified formalism for second-order classical field theories
Pedro D. Prieto-Martínez; Narciso Román-Roy
2015-06-05
We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds of systems. This model provides a straightforward and simple way to define the Poincar\\'e-Cartan form and clarifies the construction of the Legendre map (univocally obtained as a consequence of the constraint algorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the field equations, which are analyzed in-depth, and written in terms of holonomic sections and multivector fields. Our treatment therefore completes previous attempt to achieve this aim. The formulation is applied to describing some physical examples; in particular, to giving another alternative multisymplectic description of the Korteweg-de Vries equation.
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
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.}
Semiclassical Ponderomotive Lagrangian for the Dirac Electron
NASA Astrophysics Data System (ADS)
Ruiz, D. E.; Dodin, I. Y.
2014-10-01
The ponderomotive effect caused by a high-frequency electromagnetic field on a classical particle can be calculated conveniently, within a first-principle variational approach, as the Kerr effect experienced by the particle's quantum wave function in the semiclassical approximation. The previous calculations have been restricted to nonrelativistic scalar particles in weak fields. Here we extend those results to relativistic vector particles in arbitrarily strong fields. In particular, we derive the ponderomotive Lagrangian for the Dirac electron in a relativistically-intense laser wave propagating in vacuum. Classical waves in plasma can be described in a similar manner; hence our calculation also generalizes the recent ``ponderomotive'' theory of wave-wave adiabatic coupling to fully electromagnetic interactions. This work was supported by the DOE NNSA through Contract Number DE274-FG52-08NA28553.
Classical Theory of Optical Near Field
NASA Astrophysics Data System (ADS)
Banno, Itsuki
The main purpose of this chapter is to present the quasi-static picture of an optical field in the vicinity of small-scale material. The quasi-static picture depends on the fact that the induced boundary charge density dominates the optical near field of a small-scale material via Coulomb's law; therefore, such an optical near field is of a non-radiative or longitudinal nature. This simple physics leads to an intuitive understanding, even in complicated systems with magneto- and electro-optical effects. As prerequisites, the definitions of elementary concepts are given: "retardation effect," "diffraction limit," "near field," and "far field." Furthermore, two numerical methods are presented using the minimum degree of freedom of an electromagnetic field; one is described by the scalar potential adequate for a quasi-static system and the other by a dual vector potential for general optical systems. This chapter is restricted to linear optical effects and is a revised version of the article titled by "Classical Theory on Electromagnetic Near Field" in Progress in Nano-Electro-Optics II (Springer-Verlag Berlin Heidelberg, 2004).
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
F. J. Beron-Vera; M. J. Olascoaga; G. Haller; M. Farazmand; J. Trinanes; Y. Wang
2015-02-23
Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived \\emph{Sargassum} distributions.
Compressible Lagrangian hydrodynamics without Lagrangian cells
Clark, R.A.
1985-01-01
Traditional Lagrangian hydrodynamic codes for time dependent, compressible, multimaterial problems in two dimensions use the same general method. A Lagrangian mesh is defined, which moves with the fluid and this mesh defines a set of Lagrangian cells. The mass in each cell remains fixed and the motion of the mesh determines the volume and hence the density of each cell. These methods work well until the mesh becomes distorted due to shear or turbulence. Large distortions cause computer codes to quickly grind to a halt. The usual solution to distortion is to ''rezone'' the mesh. Here we move the mesh points artificially so as to reduce distortions and then map the quantities from the old mesh to the new. This results in unwanted diffusion of mass, momentum and energy throughout the mesh. Even with rezoning, few Lagrangian codes can handle more than limited distortions. Recently, what we call ''Free-Lagrangian'' codes have been developed specifically to handle large distortions. These codes, in addition to adjusting the mesh points, can reconnect mesh points, thus creating new cells. While Free-Lagrangian codes can handle virtually any distortion, they are even more diffusive than rezoners. We are trying a different aproach to the problem. We abandon the idea of Lagrangian cells entirely. In the next section we will discuss how the conservation equations can be solved directly without resorting to Lagrangian cells. Next we will give some examples of calculations using this method. Finally, we will give details of the calculational method presently being used.
Scalar Field Theories with Polynomial Shift Symmetries
Tom Griffin; Kevin T. Grosvenor; Petr Horava; Ziqi Yan
2014-12-02
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree $P$ in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree $P$, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree $P$? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of $P=1$ (essentially equivalent to Galileons), we reproduce the known Galileon $N$-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with $N$ vertices. Then we extend the classification to $P>1$ and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.
Aspects of Four Dimensional N = 2 Field Theory
Xie, Dan
2011-07-11
superconformal quiver gauge theory by putting regular singularity at the puncture. The algorithm of calculating weakly coupled gauge group in any duality frame is developed. The asymptotical free theory and Argyres-Douglas field theory can also be constructed...
Pauli-Villars regulatization of supergravity and field theory anomalies
Gaillard, M.K.
1995-06-01
A procedure for Pauli-Villars regularization of locally and globally supersymmetric theories is described. Implications for specific theories, especially those obtained from superstrings, are discussed with emphasis on the role of field theory anomalies.
Aspects of Four Dimensional N = 2 Field Theory
Xie, Dan
2011-07-11
superconformal quiver gauge theory by putting regular singularity at the puncture. The algorithm of calculating weakly coupled gauge group in any duality frame is developed. The asymptotical free theory and Argyres-Douglas field theory can also be constructed...
New mathematical structures in renormalizable quantum field theories
Dirk Kreimer
2003-01-01
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.
Classical Field Theory and Analogy Between Newton's and Maxwell's Equations
Z. Oziewicz
1993-12-02
A bivertical classical field theory include the Newtonian mechanics and Maxwell's electromagnetic field theory as the special cases. This unification allows to recognize the formal analogies among the notions of Newtonian mechanics and Maxwell's electrodynamics.
On a Mean Field Theory of Topological 2D Gravity
Jian Zhou
2015-03-30
We present a one-dimensional mean field theory for topological 2D gravity. We discuss possible generalizations to other topological field theories, in particular those related to semisimple Frobenius manifolds.
8.324 Quantum Field Theory II, Fall 2002
Hanany, Amihay
Second semester of a three-semester subject sequence on quantum field theory stressing the relativistic quantum field theories relevant to the physics of the Standard Model. Develops in depth some of the topics discussed ...
Hot Defect Superconformal Field Theory in an External Magnetic Field
Veselin G. Filev
2009-10-05
In this paper we investigate the influence of an external magnetic field on a flavoured holographic gauge theory dual to the D3/D5 intersection at finite temperature. Our study shows that the external magnetic field has a freezing effect on the confinement/ deconfinement phase transition. We construct the corresponding phase diagram. We investigate some thermodynamic quantities of the theory. A study of the entropy reveals enhanced relative jump of the entropy at the "chiral" phase transition. A study of the magnetization shows that both the confined and deconfined phases exhibit diamagnetic response. The diamagnetic response in the deconfined phase has a stronger temperature dependence reflecting the temperature dependence of the conductivity. We study the meson spectrum of the theory and analyze the stability of the different phases looking at both normal and quasi-normal semi-classical excitations. For the symmetry breaking phase we analyze the corresponding pseudo-Goldstone modes and prove that they satisfy non-relativistic dispersion relation.
A Survey of Lagrangian Mechanics and Control on Lie algebroids and groupoids
Jorge Cortes; Manuel de Leon; Juan C. Marrero; D. Martin de Diego; Eduardo Martinez
2005-11-03
In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundness of the approach.
Superconformal field theories from crystal lattices
Sangmin Lee
2006-10-24
We propose a brane configuration for the (2+1)d, $\\CN=2$ superconformal theories (CFT$_3$) arising from M2-branes probing toric Calabi-Yau 4-fold cones, using a T-duality transformation of M-theory. We obtain intersections of M5-branes on a three-torus which form a 3d bipartite crystal lattice in a way similar to the 2d dimer models for CFT$_4$. The fundamental fields of the CFT$_3$ are M2-brane discs localized around the intersections, and the super-potential terms are identified with the atoms of the crystal. The model correctly reproduces the complete BPS spectrum of mesons and baryons.
Heterotic $?$'-corrections in Double Field Theory
Oscar A. Bedoya; Diego Marques; Carmen Nunez
2014-12-15
We extend the generalized flux formulation of Double Field Theory to include all the first order bosonic contributions to the $\\alpha '$ expansion of the heterotic string low energy effective theory. The generalized tangent space and duality group are enhanced by $\\alpha'$ corrections, and the gauge symmetries are generated by the usual (gauged) generalized Lie derivative in the extended space. The generalized frame receives derivative corrections through the spin connection with torsion, which is incorporated as a new degree of freedom in the extended bein. We compute the generalized fluxes and find the Riemann curvature tensor with torsion as one of their components. All the four-derivative terms of the action, Bianchi identities and equations of motion are reproduced. Using this formalism, we obtain the first order $\\alpha'$ corrections to the heterotic Buscher rules. The relation of our results to alternative formulations in the literature is discussed and future research directions are outlined.
Lattice field theory simulations of graphene
Joaquín E. Drut; Timo A. Lähde
2009-04-21
We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling.
Working Group Report: Lattice Field Theory
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Analogies between Scaling in Turbulence, Field Theory and Critical Phenomena
Gregory Eyink; Nigel Goldenfeld
1994-07-05
We discuss two distinct analogies between turbulence and field theory. In one analogue, the field theory has an infrared attractive renormalization-group fixed point and corresponds to critical phenomena. In the other analogue, the field theory has an ultraviolet attractive fixed point, as in quantum chromodynamics.
Analogies between scaling in turbulence, field theory, and critical phenomena
Gregory Eyink; Nigel Goldenfeld
1994-01-01
We discuss two distinct analogies between turbulence and field theory. In one analog, the field theory has an infrared attractive renormalization-group fixed point and corresponds to critical phenomena. In the other analog, the field theory has an ultraviolet attractive fixed point, as in quantum chromodynamics.
Transfer operators and topological field theory
Igor V. Ovchinnikov
2014-10-24
The transfer operator (TO) formalism of the dynamical systems (DS) theory is reformulated here in terms of the recently proposed cohomological theory (ChT) of stochastic differential equations (SDE). It turns out that the stochastically generalized TO (GTO) of the DS theory is the finite-time ChT Fokker-Planck evolution operator. As a result comes the supersymmetric trivialization of the so-called sharp trace and sharp determinant of the GTO, with the former being the Witten index of the ChT. Moreover, the Witten index is also the stochastic generalization of the Lefschetz index so that it equals the Euler characteristic of the (closed) phase space for any flow vector field, noise metric, and temperature. The enabled possibility to apply the spectral theorems of the DS theory to the ChT Fokker-Planck operators allows to extend the previous picture of the spontaneous topological supersymmetry (Q-symmetry) breaking onto the situations with negative ground state's attenuation rate. The later signifies the exponential growth of the number of periodic solutions/orbits in the large time limit, which is the unique feature of chaotic behavior proving that the spontaneous breakdown of Q-symmetry is indeed the field-theoretic definition and stochastic generalization of the concept of deterministic chaos. In addition, the previously proposed low-temperature classification of SDE's, i.e., thermodynamic equilibrium / noise-induced chaos ((anti-)instanton condensation) / ordinary chaos (non-integrability), is complemented by the discussion of the high-temperature regime where the sharp boundary between the noise-induced and ordinary chaotic phases must smear out into a crossover, and at even higher temperatures the Q-symmetry is restored. An unambiguous resolution of the Ito-Stratonovich dilemma in favor of the Stratonovich approach and/or Weyl quantization is also presented.
Point-form quantum field theory
Biernat, E.P. [Institut fuer Physik, Universitaet Graz, A-8010 Graz (Austria)], E-mail: elmar.biernat@stud.uni-graz.at; Klink, W.H. [Department of Physics and Astronomy, University of Iowa, Iowa City, IA (United States)], E-mail: william-klink@uiowa.edu; Schweiger, W. [Institut fuer Physik, Universitaet Graz, A-8010 Graz (Austria)], E-mail: wolfgang.schweiger@uni-graz.at; Zelzer, S. [Institut fuer Physik, Universitaet Graz, A-8010 Graz (Austria)], E-mail: s.zelzer@dkfz-heidelberg.de
2008-06-15
We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form x{sub {mu}}x{sup {mu}} = {tau}{sup 2}. This choice of quantization surface implies that all components of the 4-momentum operator are affected by interactions (if present), whereas rotation and boost generators remain interaction free-a feature characteristic of Dirac's 'point-form' of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincare generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.
Dynamic field theory and equations of motion in cosmology
NASA Astrophysics Data System (ADS)
Kopeikin, Sergei M.; Petrov, Alexander N.
2014-11-01
We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein's equations in the form of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast ?? / ? ? 1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits ?? / ? ? 1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress-energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein's equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.
Entropy and correlators in quantum field theory
NASA Astrophysics Data System (ADS)
Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G.
2010-06-01
It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the observer's ability to probe this information experimentally, we also calculate the correction to the Gaussian entropy for two specific non-Gaussian states.
Drift estimation from a simple field theory
Mendes, F. M.; Figueiredo, A. [Instituto de Fisica, Universidade de Brasilia, CP: 04455, 70919-970-Brasilia (Brazil)
2008-11-06
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.
A new approach to unified field theories
P. Furlan; R. Raczka
1981-01-01
Summary The idea that an internal-symmetry groupG is implied by a dynamical higher space-time symmetry groupK of a given field theory is presented. Using this idea, we have classified admissible simple Lie groupsK and we have explicitly determined the internal-symmetry groupG implied byK. We have shown that the groupsG are «quantized» and in this framework they areU(2),U(4),U(8), …,U(2\\u000a N\\u000a ), depending
Thermalization of Strongly Coupled Field Theories
Balasubramanian, V. [David Rittenhouse Laboratory, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States); Bernamonti, A.; Copland, N.; Craps, B.; Staessens, W. [Theoretische Natuurkunde, Vrije Universiteit Brussel, and International Solvay Institutes, B-1050 Brussels (Belgium); Boer, J. de [Institute for Theoretical Physics, University of Amsterdam, 1090 GL Amsterdam (Netherlands); Keski-Vakkuri, E. [Helsinki Institute of Physics and Department of Physics, FIN-00014 University of Helsinki (Finland); Mueller, B. [Department of Physics and CTMS, Duke University, Durham, North Carolina 27708 (United States); Schaefer, A. [Institut fuer Theoretische Physik, Universitaet Regensburg, D-93040 Regensburg (Germany); Shigemori, M. [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan)
2011-05-13
Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.
Purely cubic action for string field theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
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.
Conformal field theories, representations and lattice constructions
NASA Astrophysics Data System (ADS)
Dolan, L.; Goddard, P.; Montague, P.
1996-07-01
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and Z 2-twisted theories, ?( ?) andtilde H(? ) respectively, which may be constructed from a suitable even Euclidean lattice ?. Similarly, one may construct lattices? _C andtilde ? _C by analogous constructions from a doubly-even binary codeC. In the case whenC is self-dual, the corresponding lattices are also. Similarly, ?( ?) andtilde H(? ) are self-dual if and only if ? is. We show thatH(? _C ) has a natural “triality” structure, which induces an isomorphismH(tilde ? _C ) ?tilde H(? _C ) and also a triality structure ontilde H(tilde ? _C ). ForC the Golay code,tilde ? _C is the Leech lattice, and the triality ontilde H(tilde ? _C ) is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories ?( ?) andtilde H(? ) with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.
Bekenstein bound in asymptotically free field theory
Arias, E.; Svaiter, N. F.; Menezes, G. [Centro Brasileiro de Pesquisas Fisicas-CBPF, Rua Dr. Xavier Sigaud 150, Rio de Janeiro, RJ, 22290-180 (Brazil); Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, Sao Paulo, SP, 01140-070 (Brazil)
2010-08-15
For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality (S/E){<=}2{pi}R, where R stands for the radius of the smallest sphere that circumscribes the system. The validity of the Bekenstein bound in the asymptotically free side of the Euclidean ({lambda}{phi}{sup 4}){sub d} scalar field theory is investigated. We consider the system in thermal equilibrium with a reservoir at temperature {beta}{sup -1} and defined in a compact spatial region without boundaries. Using the effective potential, we discuss the thermodynamic of the model. For low and high temperatures the system presents a condensate. We present the renormalized mean energy E and entropy S for the system and show in which situations the specific entropy satisfies the quantum bound.
Bondi mass in classical field theory
Jacek Jezierski
1997-03-27
We analyze three classical field theories based on the wave equation: scalar field, electrodynamics and linearized gravity. We derive certain generating formula on a hyperboloid and on a null surface for them. The linearized Einstein equations are analyzed around 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. The result gives a new interpretation of the Bondi mass loss formula. We show also how to define angular momentum. Starting from affine approach for Einstein equations we obtain variational formulae for Bondi-Sachs type metrics related with 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.
Perfect magnetohydrodynamics as a field theory
Bekenstein, Jacob D.; Betschart, Gerold [Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2006-10-15
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.
Perfect magnetohydrodynamics as a field theory
Jacob D. Bekenstein; Gerold Betschart
2006-10-16
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 $\\hbar$; 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.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
Constraining noncommutative field theories with holography
Raul Horvat; Josip Trampetic
2011-01-19
An important window to quantum gravity phenomena in low energy noncommutative (NC) quantum field theories (QFTs) gets represented by a specific form of UV/IR mixing. Yet another important window to quantum gravity, a holography, manifests itself in effective QFTs as a distinct UV/IR connection. In matching these two principles, a useful relationship connecting the UV cutoff $\\Lambda_{\\rm UV}$, the IR cutoff $\\Lambda_{\\rm IR}$ and the scale of noncommutativity $\\Lambda_{\\rm NC}$, can be obtained. We show that an effective QFT endowed with both principles may not be capable to fit disparate experimental bounds simultaneously, like the muon $g-2$ and the masslessness of the photon. Also, the constraints from the muon $g-2$ preclude any possibility to observe the birefringence of the vacuum coming from objects at cosmological distances. On the other hand, in NC theories without the UV completion, where the perturbative aspect of the theory (obtained by truncating a power series in $ \\Lambda_{\\rm NC}^{-2}$) becomes important, a heuristic estimate of the region where the perturbative expansion is well-defined $E/ \\Lambda_{\\rm NC} \\lesssim 1$, gets affected when holography is applied by providing the energy of the system $E$ a $\\Lambda_{\\rm NC}$-dependent lower limit. This may affect models which try to infer the scale $\\Lambda_{\\rm NC}$ by using data from low-energy experiments.
Radiation reaction in quantum field theory
Atsushi Higuchi
2004-03-30
We investigate radiation-reaction effects for a charged scalar particle accelerated by an external potential realized as a space-dependent mass term in quantum electrodynamics. In particular, we calculate the position shift of the final-state wave packet of the charged particle due to radiation at lowest order in the fine structure constant alpha and in the small h-bar approximation. We show that it disagrees with the result obtained using the Lorentz-Dirac formula for the radiation-reaction force, and that it agrees with the classical theory if one assumes that the particle loses its energy to radiation at each moment of time according to the Larmor formula in the static frame of the potential. However, the discrepancy is much smaller than the Compton wavelength of the particle. We also point out that the electromagnetic correction to the potential has no classical limit. (Correction. Surface terms were erroneously discarded to arrive at Eq. (59). By correcting this error we find that the position shift according to the Lorentz-Dirac theory obtained from Eq. (12) is reproduced by quantum field theory in the hbar -> 0 limit. We also find that the small V(z) approximation is unnecessary for this agreement. See Sec. VII.)
Homogeneous cosmologies as group field theory condensates
NASA Astrophysics Data System (ADS)
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2014-06-01
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.
LanHEP—a package for the automatic generation of Feynman rules in field theory. Version 3.0
NASA Astrophysics Data System (ADS)
Semenov, A. V.
2009-03-01
The LanHEP program version 3.0 for Feynman rules generation from the Lagrangian is described. It reads the Lagrangian written in a compact form, close to the one used in publications. It means that Lagrangian terms can be written with summation over indices of broken symmetries and using special symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Supersymmetric theories can be described using the superpotential formalism and the 2-component fermion notation. The output is Feynman rules in terms of physical fields and independent parameters in the form of CompHEP model files, which allows one to start calculations of processes in the new physical model. Alternatively, Feynman rules can be generated in FeynArts format or as LaTeX table. One-loop counterterms can be generated in FeynArts format. Program summaryProgram title: LanHEP Catalogue identifier: ADZV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 83 041 No. of bytes in distributed program, including test data, etc.: 1 090 931 Distribution format: tar.gz Programming language: C Computer: PC Operating system: Linux RAM: 2 MB (SM), 12 MB (MSSM), 120 MB (MSSM with counterterms) Classification: 4.4 Nature of problem: Deriving Feynman rules from the Lagrangian Solution method: The program reads the Lagrangian written in a compact form, close to the one used in publications. It means that Lagrangian terms can be written with summation over indices of broken symmetries and using special symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Tools for checking the correctness of the model, and for simplifying the output expressions are provided. The output is Feynman rules in terms of physical fields and independent parameters in the form of CompHEP model files, which allows one to start calculations of processes in the new physical model. Alternatively, Feynman rules can be generated in FeynArts format or as a LaTeX table. Running time: 1 sec (SM), 8 sec (MSSM), 8 min (MSSM with counterterms)
Quantum field theories on noncommutative R^4 versus theta-expanded quantum field theories
Raimar Wulkenhaar
2002-01-01
I recall the main motivation to study quantum field theories on noncommutative spaces and comment on the most-studied example, the noncommutative R^4. That algebra is given by the *-product which can be written in (at least) two ways: in an integral form or an exponential form. These two forms of the *-product are adapted to different classes of functions, which,
The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic Quantum Field Theory
Lee Smolin
1995-01-01
An approach to quantum gravity and cosmology is proposed based on a synthesis of four elements: 1) the Bekenstein bound and the related holographic hypothesis of 't Hooft and Susskind, 2) topological quantum field theory, 3) a new approach to the interpretational issues of quantum cosmology and 4) the loop representation formulation of non-perturbative quantum gravity. A set of postulates
Group Theoretical Approach to the Construction of Conformal Field Theories
Benjamin Horowitz
2013-12-21
A conformal field theory (CFT) is a quantum field theory which is invariant under conformal transformations; a group action that preserve angles but not necessarily lengths. There are two traditional approaches to the construction of CFTs: analyzing a statistical system near a critical point as a euclidean field theory, and in holographic duality within the context of string theory. This pedagogical paper presents a construction of CFTs using purely group theoretic techniques. Starting with the basic definition of a Lie algebra and quantum field theory, we generalize to affine Lie algebras and form a energy momentum tensor via the Sugawara construction.
Group Theoretical Approach to the Construction of Conformal Field Theories
Horowitz, Benjamin
2013-01-01
A conformal field theory (CFT) is a quantum field theory which is invariant under conformal transformations; a group action that preserve angles but not necessarily lengths. There are two traditional approaches to the construction of CFTs: analyzing a statistical system near a critical point as a euclidean field theory, and in holographic duality within the context of string theory. This pedagogical paper presents a construction of CFTs using purely group theoretic techniques. Starting with the basic definition of a Lie algebra and quantum field theory, we generalize to affine Lie algebras and form a energy momentum tensor via the Sugawara construction.
Hinterbichler, Kurt; Joyce, Austin; Khoury, Justin, E-mail: kurthi@physics.upenn.edu, E-mail: joyceau@sas.upenn.edu, E-mail: jkhoury@sas.upenn.edu [Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104 (United States)
2012-06-01
The pseudo-conformal scenario is an alternative to inflation in which the early universe is described by an approximate conformal field theory on flat, Minkowski space. Some fields acquire a time-dependent expectation value, which breaks the flat space so(4,2) conformal algebra to its so(4,1) de Sitter subalgebra. As a result, weight-0 fields acquire a scale invariant spectrum of perturbations. The scenario is very general, and its essential features are determined by the symmetry breaking pattern, irrespective of the details of the underlying microphysics. In this paper, we apply the well-known coset technique to derive the most general effective lagrangian describing the Goldstone field and matter fields, consistent with the assumed symmetries. The resulting action captures the low energy dynamics of any pseudo-conformal realization, including the U(1)-invariant quartic model and the Galilean Genesis scenario. We also derive this lagrangian using an alternative method of curvature invariants, consisting of writing down geometric scalars in terms of the conformal mode. Using this general effective action, we compute the two-point function for the Goldstone and a fiducial weight-0 field, as well as some sample three-point functions involving these fields.
Mapping of the density functional theory on the crystal field theory of rare earth systems
M. Fähnle
1995-01-01
By mapping the density functional theory on the crystal field theory within a first order perturbation approach it is proven that the exchange-correlation potential has to be included into the definition of the crystal field parameters, as suggested by Novák and coworkers. The validity of the first order theory yielding crystal field parameters which are independent of the state of
Geomagnetic Field -- From Paleomagnetism to Dynamo Theory
NASA Astrophysics Data System (ADS)
Kono, M.
2008-05-01
Since 1995, self-consistent models of the geodynamo became available. There are certain problems, but some of these models have shown behaviors quite similar to those observed by paleomagnetism, including polarity reversals (Kono and Roberts, 2002). There is thus a hope that the combination of paleomagnetism and dynamo theory may provide us a very comprehensive understanding of the geomagnetic field. In this paper, I will try to highlight the possibilities and limitations in such studies. From satellite observations, it was shown that the power of the magnetic field contained in each degree is nearly the same if measured at the core-mantle boundary (CMB). The core field can be seen only to degree 13 or 14 where the field power is about (10 nT)2. Beyond that, the crustal magnetization dominates and the core signal is lost. The value of 10 nT is far larger than the accuracy of the present-day instruments, but much smaller than the resolution obtainable by paleomagnetic observations. We may safely assume that the error in paleomagnetic measurements (in direction) is of the order of 10 degrees. This error corresponds to the resolution of about 1/5. The relative powers of the low degree terms in the magnetic field at the surface are 1.0, 0.033, 0.019, 0.0055 (Langel and Estes, 1982). This means that only the degrees 1 to 3 terms may be distinguished by paleomagnetic data. From the combination of dipole, quadrupole, and octupole, what we can deduce about the fundamental properties of the geomagnetic field? Here are some of the possibilities, which may give important clues when we compare with dynamo simulation results. (1) The current dipole power is several times larger than the value expected from the trend line produced by degrees 2--13. Is this a persistent feature or transient? (2) In PSV analysis, the angular standard deviation increases with latitude. Kono and Tanaka (1995) showed that it is possible only if the (2,1) (degree, order) or (3,2) term is very large. But the present field does not show such features. What is the solution of this difference? (3) If the dynamo is very simple, the dynamo modes may be divided into two distinct groups (dipole family and quadrupole family) due to the selection rules (Roberts and Stix, 1972). McFadden et al. (1988) derived a paleosecular variation model based on this separation. Is it a real feature?
Holographic confining gauge theory and response to the electric field
Kazuo Ghoroku; Masafumi Ishihara; Tomoki Taminato
2010-01-01
We study the response of confining gauge theory to the external electric field by using holographic Yang-Mills theories in the large Nc limit. Although the theories are in the confinement phase, we find a transition from the insulator to the conductor phase when the electric field exceeds its critical value. Then, the baryon number current is generated in the conductor
Hermeneutical Field Theory and the Structural Character of Understanding
William Leonard Whitehouse
1991-01-01
Through a series of exploratory case studies focusing on hermeneutics, phenomenology, relativity, field theory, quantum mechanics, chronobiology, chaos theory, holographic theory and various aspects of mathematics, a set of hermeneutical constraints and degrees of freedom are generated. There are a set of eight field equations given in the thesis which give qualitative symbolic expression to the aforementioned spectrum of constraints
Holographic confining gauge theory and response to the electric field
Kazuo Ghoroku; Masafumi Ishihara; Tomoki Taminato
2010-01-01
We study the response of confining gauge theory to the external electric field by using holographic Yang-Mills theories in the large N{sub c} limit. Although the theories are in the confinement phase, we find a transition from the insulator to the conductor phase when the electric field exceeds its critical value. Then, the baryon number current is generated in the
Crystal field theory and the Shubnikov point groups
Arthur P. Cracknell
1968-01-01
Two pieces of theory which have so far remained unconnected, crystal field theory and the theory of corepresentations of non-unitary groups, are brought together here for the study of the splitting of atomic energy levels in a crystalline field with the symmetry of one of the magnetic (Shubnikov) point groups. The cases of the various possible relative strengths of the
Nematic Liquid Crystals : Mean-field and Continuum theories
Lakkis, Omar
Nematic Liquid Crystals : Mean-field and Continuum theories Apala Majumdar Oxford Centre.lci.kent.edu/defect.html ) #12;Mathematical Theory · Define order parameter that distinguishes nematic liquid crystals from the lower bound for the eigenvalues physically unrealistic? 3 1 #12;Maier-Saupe Mean-Field Theory: A brief
A unified field theory of mesons and baryons
T. Skyrme; T. H. R
1962-01-01
The way in which a nonlinear meson type of field theory may contain its ; own sources, and how these may be idealized to point singularities as in the ; conventional field theories of interacting linear systems, is formulated. The ; structure of the particle source in the classical theory is caleulated, and some ; qualitative features of the interactions
Benjamin Chih-Chien Nien
2006-01-01
This paper attempts to analyze “central place theory” of spatial economics based on “supply and demand theory” in microeconomics and “field theory” in physics, and also discuss their relationship. Three most important research findings are described below. Firstly, the concept of market equilibrium could be expressed in the mathematical form of physics field theory under proper hypothesis. That is because
Benjamin Chih-Chien Nien
2006-01-01
This paper attempts to analyze central place theory of spatial economics based on supply and demand theory in microeconomics and field theory in physics, and also discuss their relationship. Three most important research findings are described below. Firstly, the concept of market equilibrium could be expressed in the mathematical form of physics field theory under proper hypothesis. That is because
Dulmet, B; Bourquin, R
2001-10-01
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
Matrix product states for gauge field theories
Boye Buyens; Jutho Haegeman; Karel Van Acoleyen; Henri Verschelde; Frank Verstraete
2014-11-03
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study non-equilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.
Quantifying truncation errors in effective field theory
Furnstahl, R J; Phillips, D R; Wesolowski, S
2015-01-01
Bayesian procedures designed to quantify truncation errors in perturbative calculations of quantum chromodynamics observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions ("priors") for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We first demonstrate the calculation of Bayesian probability distributions for the EFT truncation error in some representative examples, and then focus on the application of chiral EFT to neutron-pr...
Integrable Conformal Field Theory - A Case Study
Schomerus, Volker [DESY Hamburg, Theory Group, Notkestrasse 85, D-22607 Hamburg (Germany)
2010-06-17
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.
Generalized Gibbs ensembles for quantum field theories
NASA Astrophysics Data System (ADS)
Essler, F. H. L.; Mussardo, G.; Panfil, M.
2015-05-01
We consider the nonequilibrium dynamics in quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In the presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra)local in the usual sense of QFTs, but fulfill a significantly weaker form of locality. We discuss the implications of our results for integrable QFTs in one spatial dimension.
Neutrino Wave Packets in Quantum Field Theory
C. Giunti
2002-06-26
We present a model of neutrino oscillations in the framework of quantum field theory in which the propagating neutrino and the particles participating to the production and detection processes are described by wave packets. The neutrino state is a superposition of massive neutrino wave packets determined by the production process, as naturally expected from causality. We show that the energies and momenta of the massive neutrino components relevant for neutrino oscillations are in general different from the average energies and momenta of the propagating massive neutrino wave packets, because of the effects of the detection process. Our results confirm the correctness of the standard expression for the oscillation length of extremely relativistic neutrinos and the existence of a coherence length.
Mean field theory of charged dendrimer molecules.
Lewis, Thomas; Pryamitsyn, Victor; Ganesan, Venkat
2011-11-28
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
The Electrostatics of Einstein's Unified Field Theory
S. Antoci; D. -E. Liebscher; L. Mihich
2005-06-09
When sources are added at their right-hand sides, and g_{(ik)} is a priori assumed to be the metric, the equations of Einstein's Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_{(ik)} in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_{(ik)}, however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by H\\'ely. In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when H\\'ely's physically correct metric is adopted.
Hamiltonian constraint in polymer parametrized field theory
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
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.
AN INTRODUCTION TO FREE QUANTUM FIELD THEORY THROUGH KLEIN-GORDON THEORY
May, J. Peter
AN INTRODUCTION TO FREE QUANTUM FIELD THEORY THROUGH KLEIN-GORDON THEORY JONATHAN EMBERTON Abstract the classical form of Klein-Gordon theory. Contents 1. Introduction and Overview 1 2. Klein-Gordon Theory quantizations are performed by observing how Klein-Gordon theory and Maxwell's equations may be quantized. 2
String Calculus: Conformal Field Theory as a Tool in String Theory
Gardel, Margaret
String Calculus: Conformal Field Theory as a Tool in String Theory Emil Martinec Enrico Fermi Inst, in the guise of string theory. String theory promises an elegant synthesis of quan- tum mechanics (algebra in string theory in the description of perturbative string propagation. However, one might believe
The IR-resummed Effective Field Theory of Large Scale Structures
Leonardo Senatore; Matias Zaldarriaga
2015-02-24
We present a new method to resum the effect of large scale motions in the Effective Field Theory of Large Scale Structures. Because the linear power spectrum in $\\Lambda$CDM is not scale free the effects of the large scale flows are enhanced. Although previous EFT calculations of the equal-time density power spectrum at one and two loops showed a remarkable agreement with numerical results, they also showed a 2% residual which appeared related to the BAO oscillations. We show that this was indeed the case, explain the physical origin and show how a Lagrangian based calculation removes this differences. We propose a simple method to upgrade existing Eulerian calculations to effectively make them Lagrangian and compare the new results with existing fits to numerical simulations. Our new two-loop results agrees with numerical results up to $k\\sim 0.6 h/$Mpc to within 1% with no oscillatory residuals. We also compute power spectra involving momentum which is significantly more affected by the large scale flows. We show how keeping track of these velocities significantly enhances the UV reach of the momentum power spectrum in addition to removing the BAO related residuals. We compute predictions for the real space correlation function around the BAO scale and investigate its sensitivity to the EFT parameters and the details of the resummation technique.
Duality and braiding in twisted quantum field theory
Mauro Riccardi; Richard J. Szabo
2008-01-01
We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green's functions in the noncommutative and commutative theories, causality, and the absence of UV\\/IR mixing. We use these fields to define the functional
Neural field theory with variance dynamics.
Robinson, P A
2013-06-01
Previous neural field models have mostly been concerned with prediction of mean neural activity and with second order quantities such as its variance, but without feedback of second order quantities on the dynamics. Here the effects of feedback of the variance on the steady states and adiabatic dynamics of neural systems are calculated using linear neural field theory to estimate the neural voltage variance, then including this quantity in the total variance parameter of the nonlinear firing rate-voltage response function, and thus into determination of the fixed points and the variance itself. The general results further clarify the limits of validity of approaches with and without inclusion of variance dynamics. Specific applications show that stability against a saddle-node bifurcation is reduced in a purely cortical system, but can be either increased or decreased in the corticothalamic case, depending on the initial state. Estimates of critical variance scalings near saddle-node bifurcation are also found, including physiologically based normalizations and new scalings for mean firing rate and the position of the bifurcation. PMID:22576451
Topological field theory of dynamical systems
Ovchinnikov, Igor V. [Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, California 90095-1594 (United States)
2012-09-15
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.
Short-range entanglement and invertible field theories
Daniel S. Freed
2014-08-10
Quantum field theories with an energy gap can be approximated at long-range by topological quantum field theories. The same should be true for suitable condensed matter systems. For those with short range entanglement (SRE) the effective topological theory is invertible, and so amenable to study via stable homotopy theory. This leads to concrete topological invariants of gapped SRE phases which are finer than existing invariants. Computations in examples demonstrate their effectiveness.
Seeking the balance: Patching double and exceptional field theories
G. Papadopoulos
2014-09-29
We investigate the patching of double and exceptional field theories. In double field theory the patching conditions imposed on the spacetime after solving the strong section condition imply that the 3-form field strength $H$ is exact. A similar conclusion can be reached for the form field strengths of exceptional field theories after some plausive assumptions are made on the relation between the transition functions of the additional coordinates and the patching data of the form field strengths. We illustrate the issues that arise, and explore several alternative options which include the introduction of C-folds and of the topological geometrisation condition.
A Generally Covariant Wave Equation for Grand Unified Field Theory
Myron W. Evans
2003-01-01
A generally covariant wave equation is derived geometrically for grand unified field theory. The equation states most generally that the covariant d'Alembertian acting on the vielbein vanishes for the four fields which are thought to exist in nature: gravitation, electromagnetism, weak field and strong field. The various known field equations are derived from the wave equation when the vielbein is
The Equations of Motion in Einstein's New Unified Field Theory
Joseph Callaway
1953-01-01
It is shown that the field equations of Einstein's latest unified field theory do not lead to the Lorentz equations of motion for charged particles in an electromagnetic field, if these particles are considered to be singularities of the field. To a fourth-order approximation, the motion of such particles is not influenced by the electromagnetic field, no matter how much
Holography, chiral Lagrangian and form factor relations
Fen Zuo
2013-01-16
We perform a detailed study of mesonic properties in a class of holographic models of QCD, which is described by the Yang-Mills plus Chern-Simons action. By decomposing the 5 dimensional gauge field into resonances and integrating out the massive ones, we reproduce the Chiral Perturbative Theory Lagrangian up to ${\\cal O}(p^6)$ and obtain all the relevant low energy constants (LECs). The numerical predictions of the LECs show minor model dependence, and agree reasonably with the determinations from other approaches. Interestingly, various model-independent relations appear among them. Some of these relations are found to be the large-distance limits of universal relations between form factors of the anomalous and even-parity sectors of QCD.
Parallel computing using a Lagrangian formulation
NASA Technical Reports Server (NTRS)
Liou, May-Fun; Loh, Ching Yuen
1991-01-01
A new Lagrangian formulation of the Euler equation is adopted for the calculation of 2-D supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, a better than six times speed-up was achieved on a 8192-processor CM-2 over a single processor of a CRAY-2.
Concept of unified local field theory and nonlocality of matter
Alexander A. Chernitskii
2002-11-11
The concept of unified local field theory is considered. According to this concept the quantum description and the classical one must be the levels for investigation of some world solution of the unified field model. It is shown that in the framework of the unified local field theory there are nonlocal correlations between space separate events. Thus the experiments of Aspect type for testing of the Bell inequalities and for showing of the nonlocal correlations do not reject a possibility for description of matter with the unified local field theory. Advantages of such theory for new technologies are considered.
On the conformal field theory of the Higgs branch
Edward Witten
1997-01-01
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
Short-range interactions in an effective field theory approach for nucleon-nucleon scattering
K. A. Scaldeferri; D. R. Phillips; C. -W. Kao; T. D. Cohen
1996-10-31
We investigate in detail the effect of making the range of the ``contact'' interaction used in effective field theory (EFT) calculations of NN scattering finite. This is done in both an effective field theory with explicit pions, and one where the pions have been integrated out. In both cases we calculate NN scattering in the ${}^1 S_0$ channel using potentials which are second-order in the EFT expansion. The contact interactions present in the EFT Lagrangian are made finite by use of a square-well regulator. We find that there is an optimal radius for this regulator, at which second-order corrections to the EFT are identically zero; for radii near optimal these second-order corrections are small. The cutoff EFTs which result from this procedure appear to be valid for momenta up to about 100 MeV/c. We also find that the radius of the square well cannot be reduced to zero if the theory is to reproduce both the experimental scattering length and effective range. Indeed, we show that, if the NN potential is the sum of a one-pion exchange piece and a short-range interaction, then the short-range piece must extend out beyond 1.1 fm, regardless of its particular form.
Short-range interactions in an effective field theory approach for nucleon-nucleon scattering
Scaldeferri, K A; Kao, C W; Cohen, T D
1996-01-01
We investigate in detail the effect of making the range of the ``contact'' interaction used in effective field theory (EFT) calculations of NN scattering finite. This is done in both an effective field theory with explicit pions, and one where the pions have been integrated out. In both cases we calculate NN scattering in the ${}^1 S_0$ channel using potentials which are second-order in the EFT expansion. The contact interactions present in the EFT Lagrangian are made finite by use of a square-well regulator. We find that there is an optimal radius for this regulator, at which second-order corrections to the EFT are identically zero; for radii near optimal these second-order corrections are small. The cutoff EFTs which result from this procedure appear to be valid for momenta up to about 100 MeV/c. We also find that the radius of the square well cannot be reduced to zero if the theory is to reproduce both the experimental scattering length and effective range. Indeed, we show that, if the NN potential is the ...
17.418 Field Seminar: International Relations Theory, Spring 2009
Fravel, M. Taylor
This seminar provides an overview of the field of international relations. Each week, a different approach to explaining international relations will be examined. By surveying major concepts and theories in the field, the ...
Conformal field theory of critical Casimir interactions in 2D
Bimonte, G.
Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two-dimensional (2D) conformal field theories (CFT) we derive an exact result for the ...
Exceptional field theory. III. E[subscript 8(8)
Hohm, Olaf
We develop exceptional field theory for E[subscript 8(8)], defined on a (3 + 248)-dimensional generalized spacetime with extended coordinates in the adjoint representation of E[subscript 8(8)]. The fields transform under ...
Duality and Braiding in Twisted Quantum Field Theory
Riccardi, Mauro
2008-01-01
We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green's functions in the noncommutative and commutative theories, causality, and the absence of UV/IR mixing. We use these fields to define the functional integral formulation of twisted quantum field theory. We exploit techniques from braided tensor algebra to argue that the twisted Fock space states of these free fields obey conventional statistics. We support our claims with a detailed analysis of the modifications induced in the presence of background magnetic fields, which induces additional twists by magnetic translation operators and alters the effective noncommutative geometry seen by the twisted quantum fields. When two such field theories are dual to one another, we demonstrate that only our braided physical states are cova...
Duality and braiding in twisted quantum field theory
NASA Astrophysics Data System (ADS)
Riccardi, Mauro; Szabo, Richard J.
2008-01-01
We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green's functions in the noncommutative and commutative theories, causality, and the absence of UV/IR mixing. We use these fields to define the functional integral formulation of twisted quantum field theory. We exploit techniques from braided tensor algebra to argue that the twisted Fock space states of these free fields obey conventional statistics. We support our claims with a detailed analysis of the modifications induced in the presence of background magnetic fields, which induces additional twists by magnetic translation operators and alters the effective noncommutative geometry seen by the twisted quantum fields. When two such field theories are dual to one another, we demonstrate that only our braided physical states are covariant under the duality.
Duality and Braiding in Twisted Quantum Field Theory
Mauro Riccardi; Richard J. Szabo
2007-12-10
We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green's functions in the noncommutative and commutative theories, causality, and the absence of UV/IR mixing. We use these fields to define the functional integral formulation of twisted quantum field theory. We exploit techniques from braided tensor algebra to argue that the twisted Fock space states of these free fields obey conventional statistics. We support our claims with a detailed analysis of the modifications induced in the presence of background magnetic fields, which induces additional twists by magnetic translation operators and alters the effective noncommutative geometry seen by the twisted quantum fields. When two such field theories are dual to one another, we demonstrate that only our braided physical states are covariant under the duality.
The gauge algebra of double field theory and Courant brackets
Hull, Chris
We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are constrained fields on the ...
Quantization Failure in Unified Field Theories
Daniel C. Galehouse
1995-01-01
Studies of geometrical theories suggest that fundmental problems of quantization arise from the disparate usage of displacement operators. These may be the source of a concealed inconsistency in the accepted formalism of quantum physics. General relativity and related theories cannot be quantized by the classical procedure. It is necessary to avoid the construction of differential equations by operators applied algebraically. For such theories, Von Neumann's theorem concerning hidden variables is avoided. A specified alternative class of gravitational-quantum-electrodynamic theories is possible.
Logarithmic conformal field theory: a lattice approach
NASA Astrophysics Data System (ADS)
Gainutdinov, A. M.; Jacobsen, J. L.; Read, N.; Saleur, H.; Vasseur, R.
2013-12-01
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.
Gravitational Descendants in Symplectic Field Theory
NASA Astrophysics Data System (ADS)
Fabert, Oliver
2011-02-01
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 (
Quantifying truncation errors in effective field theory
R. J. Furnstahl; N. Klco; D. R. Phillips; S. Wesolowski
2015-06-03
Bayesian procedures designed to quantify truncation errors in perturbative calculations of quantum chromodynamics observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions ("priors") for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We first demonstrate the calculation of Bayesian probability distributions for the EFT truncation error in some representative examples, and then focus on the application of chiral EFT to neutron-proton scattering. Epelbaum, Krebs, and Mei{\\ss}ner recently articulated explicit rules for estimating truncation errors in such EFT calculations of few-nucleon-system properties. We find that their basic procedure emerges generically from one class of naturalness priors considered, and that all such priors result in consistent quantitative predictions for 68% DOB intervals. We then explore several methods by which the convergence properties of the EFT for a set of observables may be used to check the statistical consistency of the EFT expansion parameter.
Gravitational consequences of modern field theories
NASA Technical Reports Server (NTRS)
Horowitz, Gary T.
1989-01-01
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.
Diffusion of Brownian particles and Liouville field theory
Franco Ferrari; Jaroslaw Paturej
2009-05-22
In this work we review a recently proposed transformation which is useful in order to simplify non-polynomial potentials given in the form of an exponential. As an application, it is shown that the Liouville field theory may be mapped into a field theory with a polynomial interaction between two scalar fields and a massive vector field. The used methodology is illustrated with the help of the simple case of a particle performing a random walk in a delta function potentials.
D-Branes, Tachyons, and String Field Theory
Washington Taylor; Barton Zwiebach
2003-01-01
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
From Quantum Gravity to Quantum Field Theory via Noncommutative Geometry
Johannes Aastrup; Jesper M. Grimstrup
2011-05-01
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The interaction involves flux tubes of the gravitational field. In the additional limit where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges.
Benjamin Chih-Chien Nien
2006-10-11
This paper attempts to analyze central place theory of spatial economics based on supply and demand theory in microeconomics and field theory in physics, and also discuss their relationship. Three most important research findings are described below. Firstly, the concept of market equilibrium could be expressed in the mathematical form of physics field theory under proper hypothesis. That is because the most important aspect of field theory model is that complex analysis is taken as a key mathematical tool. If assuming that imaginary part is neglected in this model, it is found that this model has the same mathematical structure as supply and demand theory of microeconomics. Secondly, the mathematical model of field theory can be applied to express clearly many concepts of central place theory, or even introduce many new concepts. Thirdly, it could also be taken as a study of combining the Hotelling Model and Moses Model for the location theory in another mathematic approach.
Extended gyrokinetic field theory for time-dependent magnetic confinement fields
Sugama, H.; Watanabe, T.-H.; Nunami, M. [National Institute for Fusion Science, Toki 509-5292 (Japan)] [National Institute for Fusion Science, Toki 509-5292 (Japan)
2014-01-15
A gyrokinetic system of equations for turbulent toroidal plasmas in time-dependent axisymmetric background magnetic fields is derived from the variational principle. Besides governing equations for gyrocenter distribution functions and turbulent electromagnetic fields, the conditions which self-consistently determine the background magnetic fields varying on a transport time scale are obtained by using the Lagrangian, which includes the constraint on the background fields. Conservation laws for energy and toroidal angular momentum of the whole system in the time-dependent background magnetic fields are naturally derived by applying Noether's theorem. It is shown that the ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work agree with the results from the conventional recursive formulation with the WKB representation except that collisional effects are disregarded here.
Neutron stars in the BPS Skyrme model: mean-field limit vs. full field theory
C. Adam; C. Naya; J. Sanchez-Guillen; R. Vazquez; A. Wereszczynski
2015-03-10
Using a solitonic model of nuclear matter, the BPS Skyrme model, we compare neutron stars obtained in the full field theory, where gravitational back reaction is completely taken into account, with calculations in a mean-field approximation using the Tolman-Oppenheimer-Volkoff approach. In the latter case, a mean-field-theory equation of state is derived from the original BPS field theory. We show that in the full field theory, where the energy density is non-constant even at equilibrium, there is no universal and coordinate independent equation of state of nuclear matter, in contrast to the mean-field approximation. We also study how neutron star properties are modified by going beyond mean field theory, and find that the differences between mean field theory and exact results can be considerable.
Neutron stars in the BPS Skyrme model: mean-field limit vs. full field theory
Adam, C; Sanchez-Guillen, J; Vazquez, R; Wereszczynski, A
2015-01-01
Using a solitonic model of nuclear matter, the BPS Skyrme model, we compare neutron stars obtained in the full field theory, where gravitational back reaction is completely taken into account, with calculations in a mean-field approximation using the Tolman-Oppenheimer-Volkoff approach. In the latter case, a mean-field-theory equation of state is derived from the original BPS field theory. We show that in the full field theory, where the energy density is non-constant even at equilibrium, there is no universal and coordinate independent equation of state of nuclear matter, in contrast to the mean-field approximation. We also study how neutron star properties are modified by going beyond mean field theory, and find that the differences between mean field theory and exact results can be considerable.
Mean-field theory for Bose-Hubbard model under a magnetic field
Oktel, M. Oe.; Tanatar, B. [Department of Physics, Bilkent University, 06800 Bilkent, Ankara (Turkey); Nita, M. [Institute of Physics and Technology of Materials, P.O. Box MG7, Bucharest-Magurele (Romania)
2007-01-15
We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.
Multi-field inflation: Formulation, effective theory and phenomenology
NASA Astrophysics Data System (ADS)
Gong, J.-O.
2014-03-01
We have described how to obtain the non-perturbative low energy effective field theory of single field inflation from a generic multi-field model by integrating out heavy fields. The features of heavy physics is described by the effective speed of sound, which leaves distinctive observational signatures in the correlation functions of the curvature perturbation.
Dynamics of polymers: A mean-field theory
Fredrickson, Glenn H. [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States) [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States); Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States); Department of Materials, University of California, Santa Barbara, California 93106 (United States); Orland, Henri [Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex (France)] [Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex (France)
2014-02-28
We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ? and a conjugate MSR response field ?, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamics involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.
On ramification theory in the imperfect residue field case
Zhukov, I B [St. Petersburg State University, St. Petersburg (Russian Federation)
2003-12-31
This paper is devoted to the ramification theory of complete discrete valuation fields such that the residue field has prime characteristic p and the cardinality of a p-base is 1. This class contains two-dimensional local and local-global fields. A new definition of ramification filtration for such fields is given. It turns out that Hasse-Herbrand type functions can be defined with all the usual properties. Thanks to this, a theory of upper ramification groups and the ramification theory of infinite extensions can be developed. The case of two-dimensional local fields of equal characteristic is studied in detail. A filtration on the second K-group of the field in question is introduced that is different from the one induced by the standard filtration on the multiplicative group. The reciprocity map of two-dimensional local class field theory is proved to identify this filtration with the ramification filtration.
Lattice p-Form Electromagnetism and Chain Field Theory
Derek K. Wise
2005-10-08
Since Wilson's work on lattice gauge theory in the 1970s, discrete versions of field theories have played a vital role in fundamental physics. But there is recent interest in certain higher dimensional analogues of gauge theory, such as p-form electromagnetism, including the Kalb-Ramond field in string theory, and its nonabelian generalizations. It is desirable to discretize such `higher gauge theories' in a way analogous to lattice gauge theory, but with the fundamental geometric structures in the discretization boosted in dimension. As a step toward studying discrete versions of more general higher gauge theories, we consider the case of p-form electromagnetism. We show that discrete p-form electromagnetism admits a simple algebraic description in terms of chain complexes of abelian groups. Moreover, the model allows discrete spacetimes with quite general geometry, in contrast to the regular cubical lattices usually associated with lattice gauge theory. After constructing a suitable model of discrete spacetime for p-form electromagnetism, we quantize the theory using the Euclidean path integral formalism. The main result is a description of p-form electromagnetism as a `chain field theory' -- a theory analogous to topological quantum field theory, but with chain complexes replacing manifolds. This, in particular, gives a notion of time evolution from one `spacelike slice' of discrete spacetime to another.
An application of neutrix calculus to quantum field theory
Y. Jack Ng; H. van Dam
2005-02-17
Neutrices are additive groups of negligible functions that do not contain any constants except 0. Their calculus was developed by van der Corput and Hadamard in connection with asymptotic series and divergent integrals. We apply neutrix calculus to quantum field theory, obtaining finite renormalizations in the loop calculations. For renormalizable quantum field theories, we recover all the usual physically observable results. One possible advantage of the neutrix framework is that effective field theories can be accommodated. Quantum gravity theories appear to be more manageable.
Is quantum field theory a generalization of quantum mechanics?
A. V. Stoyanovsky
2009-09-10
We construct a mathematical model analogous to quantum field theory, but without the notion of vacuum and without measurable physical quantities. This model is a direct mathematical generalization of scattering theory in quantum mechanics to path integrals with multidimensional trajectories (whose mathematical interpretation has been given in a previous paper). In this model the normal ordering of operators in the Fock space is replaced by the Weyl-Moyal algebra. This model shows to be useful in proof of various results in quantum field theory: one first proves these results in the mathematical model and then "translates" them into the usual language of quantum field theory by more or less "ugly" procedures.
Entanglement entropy in Galilean conformal field theories and flat holography.
Bagchi, Arjun; Basu, Rudranil; Grumiller, Daniel; Riegler, Max
2015-03-20
We present the analytical calculation of entanglement entropy for a class of two-dimensional field theories governed by the symmetries of the Galilean conformal algebra, thus providing a rare example of such an exact computation. These field theories are the putative holographic duals to theories of gravity in three-dimensional asymptotically flat spacetimes. We provide a check of our field theory answers by an analysis of geodesics. We also exploit the Chern-Simons formulation of three-dimensional gravity and adapt recent proposals of calculating entanglement entropy by Wilson lines in this context to find an independent confirmation of our results from holography. PMID:25839258
Noncommutative field theory with the Wick-Voros product
Salvatore Galluccio; Fedele Lizzi; Patrizia Vitale
2008-10-14
We study the noncommutative scalar field theory in the presence of the Wick-Voros product (or normally ordered product), a variant of the more studied Moyal product. We discuss both the classical and the quantum field theory in the quartic potential case, and calculate the Green's functions up to one loop, for the two and four points cases.
Tadpoles and closed string backgrounds in open string field theory
Ian Ellwood; Jessie Shelton; Washington Taylor
2003-01-01
We investigate the quantum structure of Witten's cubic open bosonic string field theory by computing the one-loop contribution to the open string tadpole using both oscillator and conformal field theory methods. We find divergences and a breakdown of BRST invariance in the tadpole diagram arising from tachyonic and massless closed string states, and we discuss ways of treating these problems.
The quantum field theory interpretation of quantum mechanics
Alberto C. de la Torre
2015-03-02
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
On the UV renormalizability of noncommutative field theories
Swarnendu Sarkar
2002-01-01
UV\\/IR mixing is one of the most important features of noncommutative field theories. As a consequence of this coupling of the UV and IR sectors, the configuration of fields at the zero momentum limit in these theories is a very singular configuration. We show that the renormalization conditions set at a particular momentum configuration with a fixed number of zero
Introduction to the Effective Field Theory Description of Gravity
John F. Donoghue
1995-01-01
This is a pedagogical introduction to the treatment of general relativity as\\u000aa quantum effective field theory. Gravity fits nicely into the effective field\\u000atheory description and forms a good quantum theory at ordinary energies.
A Weak Gravity Conjecture for Scalar Field Theories
Miao Li; Wei Song; Yushu Song; Tower Wang
2007-06-27
We show that the recently proposed weak gravity conjecture\\cite{AMNV0601} can be extended to a class of scalar field theories. Taking gravity into account, we find an upper bound on the gravity interaction strength, expressed in terms of scalar coupling parameters. This conjecture is supported by some two-dimensional models and noncommutative field theories.
The unified field theory of elementary particles: Some recent advances
W. Heisenberg
1974-01-01
Progress in the unified field theory of elementary particles over the last seven years includes experimental verification of the scale group and its application in theoretical investigations; connecting the unified field theory with phenomenological current aIgebra; exploring the consequences of the indefinite metric for the problem of causality and the classification of leptons; elaboration of methods for the calculation of
Relativistic field theory of neutron stars and their hyperon populations
Glendenning, N.K.
1986-01-01
The nuclear many-body problem is examined by means of the formulation of an effective relativistic field theory of interacting hadrons. A relativistic field theory of hadronic matter is especially appropriate for the description of hot or dense matter, because of the appearance of antiparticles and higher baryon resonances and because it automatically respects causality. 8 refs., 7 figs., 1 tab. (WRF)
Investigations of AN Alternative Theory of Gravitation
Robert Bruce Mann
1982-01-01
A theory of gravitation, in which the metric of spacetime is non-symmetric and the structure of spacetime is non-Riemannian, is investigated. The foundations of the theory are discussed, and the Lagrangian and field equations (with sources) are presented. It is shown that the Lagrangian is invariant under a U(1) gauge transformation, which allows the introduction of a conserved fermion number
Pure Geometric Field Theory: Description of Gravity and Material Distribution
M. I. Wanas; Nabil L. Youssef; W. El Hanafy
2015-03-31
A field theory is constructed in the context of parameterized absolute parallelism\\linebreak geometry. The theory is shown to be a pure gravity one. It is capable of describing the gravitational field and a material distribution in terms of the geometric structure of the geometry used (the parallelization vector fields). Three tools are used to attribute physical properties to the geometric objects admitted by the theory. Poisson and Laplace equations are obtained in the linearized version of the theory. The spherically symmetric solution of the theory, in free space, is found to coincide with the Schwarzschild exterior solution of the general theory of relativity. The theory respects the weak equivalence principle in free space only. Gravity and material distribution are not minimally coupled.
The ultraviolet Behaviour of Integrable Quantum Field Theories, Affine Toda Field Theory
A. Fring; C. Korff; B. J. Schulz
1999-02-03
We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affine Toda field theory and whose statistical interaction is of a general Haldane type. Up to the first leading order, we provide general approximated analytical expressions for the solutions of these equations from which we derive general formulae for the ultraviolet scaling functions for theories in which the underlying Lie algebra is simply laced. For several explicit models we compare the quality of the approximated analytical solutions against the numerical solutions. We address the question of existence and uniqueness of the solutions of the TBA-equations, derive precise error estimates and determine the rate of convergence for the applied numerical procedure. A general expression for the Fourier transformed kernels of the TBA-equations allows to derive the related Y-systems and a reformulation of the equations into a universal form.
The Field Line Resonance: Observation and Theory
NASA Astrophysics Data System (ADS)
Fenrich, Frances Rose Erna
This thesis is an observational and theoretical study of field line resonances (FLRs) found to occur on magnetic shells in the Earth's magnetosphere. These resonances are actually standing shear Alfven waves in the ultra-low frequency (ULF) regime, generated through mode coupling to fast compressional magnetohydrodynamic waves in the outer magnetosphere. FLRs may be signatures of fundamental processes by which energy is transported from the solar wind to the ionosphere and it is therefore important to study their characteristics and fully understand their generation mechanisms. Numerous FLR events have been identified and analyzed using the Super Dual Auroral Radar Network (SuperDARN). This network is a system of high-frequency (HF) radars which provides a global-scale view of the plasma convection in the F-region of the high-latitude ionosphere. The oscillations in plasma flow associated with an FLR are superimposed upon the background convective flow and can be used to determine many characteristics of the FLR such as frequency, phase, location, and propagation velocities. A compilation of the observations has yielded some very interesting results. The most notable of these is that the FLRs repeatedly occur at the same discrete and stable frequencies, i.e., 1.3, 1.9, and 2.5 mHz, independent of local time and azimuthal wave number, m. They are also classifiable into two distinct types: those with small azimuthal wave number (m<17), and those with large azimuthal wave number (m>17). The fact that the two different wave types have numerous similarities is very important since it suggests that the same driving mechanism is responsible for the initiation of both types of resonance. The apparent growth rates of the FLRs show a striking correlation with the azimuthal wave number of the resonance. The observed high-m resonances have amplitudes that increase with time, indicating positive growth rates, while the low-m resonances have decreasing amplitudes, indicating negative growth rates. The resonance growth rates and latitudinal phase shifts, a decrease for low-m modes and an increase for high-m modes, are found to be determined by the direction of the Poynting flux in the system. In the case of the high-m resonance, an internal driver is present which is able to couple to the system and give Poynting flux out of the resonance region. The internal driver is most likely in the form of a wave-particle interaction. The final portion of this thesis concerns the development of a theoretical model for the FLR driving mechanism. The most commonly accepted theory, the magnetospheric waveguide/cavity mode model, postulates that the magnetosphere acts as a waveguide or cavity which can generate a set of monochromatic fast wave eigenmodes which then couple to the FLRs. A review of this theory has shown that it falls short of explaining many of the experimental observations. Thus alternate theories capable of explaining the observations are explored. A new model, the magnetosheath waveguide model, is examined in detail and is shown to be very successful in its ability to explain the existence of the discrete FLRs.
An Index for Non-relativistic Superconformal Field Theories
Yu Nakayama
2009-03-05
We study the highest-weight representation of N=2 supersymmetric Schrodinger algebra which appears in non-relativistic superconformal field theories in (1+2) dimension. We define the index for the non-relativistic superconformal field theories and study its properties. As a concrete example, we compute the index for the non-relativistic limit of N=6 superconformal Chern-Simons-matter theory recently proposed by Aharony et al.
Covariant Hamiltonian Field Theories on Manifolds with Boundary: Yang-Mills Theories
Alberto Ibort; Amelia Spivak
2015-06-01
The multisymplectic formalism for first order covariant Hamiltonian field theories on manifolds with boundary is described and a general geometric formalism for the theory of boundary conditions based on the preservation of the conservation laws along the boundary is presented. This approach provides a natural geometrical realization of Fock's description of field theories as used for instance in recent work by Cattaneo, Mnev and Reshetikhin [Ca14]. The notions of the theory will be tested against three significant examples: scalar fields, Poisson sigma model and Yang-Mills theories.
Outline of a generally covariant quantum field theory and a quantum theory of gravity
Carlo Rovelli
1995-01-01
We study a tentative generally covariant quantum field theory, denoted the T-Theory, as a tool to investigate the consistency of quantum general relativity. The theory describes the gravitational field and a minimally coupled scalar field; it is based on the loop representation, and on a certain number of quantization choices. Four-dimensional diffeomorphism-invariant quantum transition probabilities can be computed from the
Unified field theory on the basis of the projective theory of relativity
G. Lessner
1982-01-01
A unified field theory is developed on the basis of the five-dimensional vacuum equations Rmunu=0 in the projective theory of relativity. The four-dimensional field equations following from Rmunu=0 by projection are a generalized Einstein-Maxwell theory, for which the generalization is given by a scalar field. The particle concept based on these equations represents the intrinsic particle properties, which are the
Hanno Essen
2007-10-24
Darwin (1920) noted that when radiation can be neglected it should be possible to eliminate the radiation degrees-of-freedom from the action of classical electrodynamics and keep the discrete particle degrees-of-freedom only. Darwin derived his well known Lagrangian by series expansion in $v/c$ keeping terms up to order $(v/c)^2$. Since radiation is due to acceleration the assumption of low speed should not be necessary. A Lagrangian is suggested that neglects radiation without assuming low speed. It cures deficiencies of the Darwin Lagrangian in the ultra-relativistic regime.
Renormalizable 1\\/Nf expansion for field theories in extra dimensions
Dmitri I. Kazakov; Grigory S. Vartanov
2007-01-01
We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional field theories. It is based on 1\\/Nf-expansion and results in a logarithmically divergent perturbation theory in arbitrary high space-time dimension. First, we consider a simple example of N-component scalar filed theory and then extend this approach to Abelian and non-Abelian gauge theories with Nf fermions. In
Composite fermion wavefunctions derived by conformal field theory
NASA Astrophysics Data System (ADS)
Cappelli, Andrea
2013-01-01
The Jain theory of hierarchical Hall states is reconsidered in the light of recent analyses that have found exact relations between projected Jain wavefunctions and conformal field theory correlators. We show that the underlying conformal theory is precisely given by the W-infinity minimal models introduced earlier. This theory involves a reduction of the multicomponent Abelian theory that is similar to the projection to the lowest Landau level in the Jain approach. The analysis closely parallels the bosonic conformal theory description of the Pfaffian and Read-Rezayi states.
Magnetism and rotation in relativistic field theory
Kazuya Mameda; Arata Yamamoto
2015-04-22
We investigate the analogy between magnetism and rotation in relativistic theory. In nonrelativistic theory, the exact correspondence between magnetism and rotation is established in the presence of an external trapping potential. Based on this, we analyze relativistic rotation under external trapping potentials. A Landau-like quantization is obtained by considering an energy-dependent potential.
Quantum field theory: Finiteness and Effectiveness
Jifeng Yang
1998-01-01
A new attempt is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the modern standard point of view. This approach works for any interaction model and space-time dimension. It is much simpler in principle and in
An Algebraic Approach to Quantum Field Theory
Rudolf Haag; Daniel Kastler
1964-01-01
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
Near-field frequency - Domain theory for propeller noise
D. B. Hanson
1983-01-01
Near-field noise equations are developed from the author's helicoidal surface theory for propeller aerodynamics and noise. Thickness, steady loading, and quadrupole sources are included. Apart from the thin blade approximation and neglect of radial source terms, the equations are exact. In a comparison with the previously published far-field theory, it is shown that several valuable features of the far-field equations
Thermodynamics of String Field Theory Motivated Nonlocal Models
Tirthabir Biswas; Joseph Kapusta; Abraham Reddy
2013-01-15
We investigate the thermodynamic properties of the nonlocal tachyon motivated by their nonlocal structure in string field theory. We use previously developed perturbative methods for nonlocal fields to calculate the partition function and the equation of state in the high temperature limit. We find that in these models the tachyons undergo a second order phase transition. We compare our results with those of ordinary scalar field theory. We also calculate the one loop finite temperature effective potential.
Exact solution of quantum field theory on noncommutative phase spaces
Edwin Langmann; Richard J. Szabo; Konstantin Zarembo
2004-01-01
We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal star-product. Explicit results are presented for all Green's functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed non-perturbatively and
Tilman Sauer
2006-01-01
A historical account of Einstein's Fernparallelismus approach toward a unified field theory of gravitation and electromagnetism is given. In this theory, a space–time characterized by a curvature-free connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field, is investigated. The approach was pursued by Einstein in a number of publications that appeared in
A class of effective field theory models of cosmic acceleration
Bloomfield, Jolyon K.; Flanagan, Éanna É., E-mail: jkb84@cornell.edu, E-mail: eef3@cornell.edu [Center for Radiophysics and Space Research, Cornell University, Space Science Building, Ithaca, NY 14853 (United States)
2012-10-01
We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher derivative terms and exploiting the field redefinition freedom, we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found in similar theories of single-field inflation, where matter is not present. We discuss several different representations of the theory that can be obtained using the field redefinition freedom. For perturbations to the quintessence field today on subhorizon lengthscales larger than the Compton wavelength of the heavy fields, the theory is weakly coupled and natural in the sense of t'Hooft. The theory admits a regime where the perturbations become modestly nonlinear, but very strong nonlinearities lie outside its domain of validity.
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt [School of Mathematics, Statistics, and Operations Research, Victoria University of Wellington, Wellington 6140 (New Zealand)
2009-07-15
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just 'how much' Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [Phys. Rev. D 79, 084008 (2009)] on 3+1 dimensional quantum gravity.
Lagrangians for biological models
M. C. Nucci; K. M. Tamizhmani
2011-08-10
We show that a method presented in [S.L. Trubatch and A. Franco, Canonical Procedures for Population Dynamics, J. Theor. Biol. 48 (1974), 299-324] and later in [G.H. Paine, The development of Lagrangians for biological models, Bull. Math. Biol. 44 (1982) 749-760] for finding Lagrangians of classic models in biology, is actually based on finding the Jacobi Last Multiplier of such models. Using known properties of Jacobi Last Multiplier we show how to obtain linear Lagrangians of those first-order systems and nonlinear Lagrangian of the corresponding single second-order equations that can be derived from them, even in the case where those authors failed such as the host-parasite model.
Spinor fields in Causal Set Theory
Roman Sverdlov
2008-01-01
The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus additional scalar fields. Grassmann nature is being enforced by allowing measure to take both positive and negative values, and
Theory of Classical Higgs Fields. III. Metric-affine gauge theory
G. Sardanashvily; A. Kurov
2014-12-11
We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $P\\to X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/H\\to X$ are treated as classical Higgs fields. Its most comprehensive example is metric-affine gauge theory on the category of natural bundles where gauge fields are general linear connections on a manifold $X$, classical Higgs fields are arbitrary pseudo-Riemannian metrics on $X$, and matter fields are spinor fields. In particular, this is the case of gauge gravitation theory.
Semiclassical theory of unimolecular dissociation induced by a laser field
NASA Technical Reports Server (NTRS)
Yuan, J.-M.; George, T. F.
1978-01-01
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.
Theory of Two Threshold Fields for Relativistic Runaway Electrons
NASA Astrophysics Data System (ADS)
Aleynikov, Pavel; Breizman, Boris N.
2015-04-01
This Letter presents a rigorous kinetic theory for relativistic runaway electrons in the near critical electric field in tokamaks. The theory provides a distribution function of the runaway electrons, reveals the presence of two different threshold electric fields, and describes a mechanism for hysteresis in the runaway electron avalanche. Two different threshold electric fields characterize a minimal field required for sustainment of the existing runaway population and a higher field required for the avalanche onset. The near-threshold regime for runaway electrons determines the time scale of toroidal current decay during runaway mitigation in tokamaks.
Decoherence in Field Theory General Couplings and Slow Quenches
Lombardo, F C; Rivers, R J
2003-01-01
We study the onset of a classical order parameter after a second-order phase transition in quantum field theory. We consider a quantum scalar field theory in which the system-field (long-wavelength modes), interacts with its environment, represented both by a set of scalar fields and by its own short-wavelength modes. We compute the decoherence times for the system-field modes and compare them with the other time scales of the model. We analyze different couplings between the system and the environment for both instantaneous and slow quenches. Within our approximations decoherence is in general a short time event.
String field theory and tachyon dynamics
Yang, Haitang, Ph. D. Massachusetts Institute of Technology
2006-01-01
In this thesis we present some works done during my doctoral studies. These results focus on two directions. The first one is motivated by tachyon dynamics in open string theory. We calculate the stress tensors for the ...
Lagrangians for plasmas in the drift-fluid approximation
NASA Astrophysics Data System (ADS)
Pfirsch, Dieter; Correa-Restrepo, Darío
1997-04-01
For drift waves and related instabilities, conservation laws can play a crucial role. In an ideal theory these conservation laws are guaranteed when a Lagrangian can be found from which the equations for the various quantities result by Hamilton's principle. Such a Lagrangian for plasmas in the drift-fluid approximation was obtained by a heuristic method in a recent paper by Pfirsch and Correa-Restrepo. In the present paper the same Lagrangian is derived from the exact multifluid Lagrangian via an iterative approximation procedure which resembles the standard method usually applied to the equations of motion. That method, however, does not guarantee that all the conservation laws hold.
Perturbative Aspects of Low-Dimensional Quantum Field Theory
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
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}.
A Theory of Antenna Electromagnetic Near Field—Part II
Said M. Mikki; Yahia M. M. Antar
2011-01-01
We continue in this paper a comprehensive theory of antenna near fields inaugurated in Part I. The concept of near- field streamlines is introduced using the Weyl expansion in which the total field is decomposed into propagating and nonpropagating parts. This process involves a breaking of the rotational symmetry of the scalar Greens function that originally facilitated the deriva- tion
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L. [Departamento de Quimica Fisica, Universidad del Pais Vasco-Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao (Spain); Egusquiza, I. L. [Departamento de Fisica Teorica, Universidad del Pais Vasco-Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao (Spain); Gerritsma, R.; Roos, C. F. [Institut fuer Quantenoptik und Quanteninformation, Oesterreichische Akademie der Wissenschaften, Otto-Hittmair-Platz 1, A-6020 Innsbruck (Austria); Institut fuer Experimentalphysik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria); Garcia-Ripoll, J. J. [Instituto de Fisica Fundamental, CSIC, Serrano 113-bis, 28006 Madrid (Spain); Solano, E. [Departamento de Quimica Fisica, Universidad del Pais Vasco-Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, Alameda Urquijo 36, 48011 Bilbao (Spain)
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Some exact results on tachyon condensation in string field theory
David Kutasov; Marcos Mariño; Gregory Moore
2000-01-01
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
Towards a unified field theory for classical electrodynamics
Towards a unified field theory for classical electrodynamics Vieri Benci , Donato Fortunato of 1934 Born and Infeld wrote [6]: 1 #12;The relation of matter and the electromagnetic field can be in one physical entity, the electromagnetic field. The particles of matter are considered
UNIFIED FIELD THEORY AND PRINCIPLE OF REPRESENTATION INVARIANCE
Wang, Shouhong
UNIFIED FIELD THEORY AND PRINCIPLE OF REPRESENTATION INVARIANCE TIAN MA AND SHOUHONG WANG Abstract. This is part of a research program to establish a unified field model for interactions in nature. The aim mathematical foundation for PRI, and to use PRI to refine the unified field equations of four interactions
Lorentz-preserving fields in Lorentz-violating theories
Oindrila Ganguly; Debashis Gangopadhyay; Parthasarathi Majumdar
2011-11-03
We identify a fairly general class of field configurations (of spins 0, 1/2 and 1) which preserve Lorentz invariance in effective field theories of Lorentz violation characterized by a constant timelike vector. These fields concomitantly satisfy the equations of motion yielding cubic dispersion relations similar to those found earlier. They appear to have prospective applications in inflationary scenarios.
Rational SFT, linearized Legendrian contact homology, and Lagrangian Floer cohomology
Ekholm, Tobias
2009-01-01
We relate the version of rational Symplectic Field Theory for exact Lagrangian cobordisms introduced in [5] with linearized Legendrian contact homology. More precisely, if $L\\subset X$ is an exact Lagrangian submanifold of an exact symplectic manifold with convex end $\\Lambda\\subset Y$, where $Y$ is a contact manifold and $\\Lambda$ is a Legendrian submanifold, and if $L$ has empty concave end, then the linearized Legendrian contact cohomology of $\\Lambda$, linearized with respect to the augmentation induced by $L$, equals the rational SFT of $(X,L)$. Following ideas of P. Seidel, this equality in combination with a version of Lagrangian Floer cohomology of $L$ leads us to a conjectural exact sequence which in particular implies that if $X=\\C^{n}$ then the linearized Legendrian contact cohomology of $\\Lambda\\subset S^{2n-1}$ is isomorphic to the singular homology of $L$. We outline a proof of the conjecture and show how to interpret the duality exact sequence for linearized contact homology of [6] in terms of ...
Frame-like Lagrangians and presymplectic AKSZ-type sigma models
NASA Astrophysics Data System (ADS)
Alkalaev, Konstantin; Grigoriev, Maxim
2014-07-01
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.
Ordinary versus PT-symmetric ?³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-01
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric ig?³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian g?³ quantum field theory with those of the PT-symmetric ig?³ quantum field theory. It is shown that while the conventional g?³ theory in d=6 dimensions is asymptotically free, the ig?³ theory is like a g?? theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
Jun-Chen Su
2006-08-19
~It is shown that the quantum massive non-Abelian field theory established in the former papers is renormalizable. This conclusion is achieved with the aid of the Ward-Takahashi identities satisfied by the generating functionals which were derived in the preceding paper based on the BRST-symmetry of the theory. By the use of the Ward-Takahashi identity, it is proved that the divergences occurring in the perturbative calculations for the massive gauge field theory can be eliminated by introducing a finite number of counterterms in the effective action. As a result of the proof, it is found that the renormalization constants for the massive gauge field theory comply with the same Slavnov-Taylor identity as that for the massless gauge field theory. The latter identity is re-derived from the Ward-Takahashi identities satisfied by the gluon proper vertices and their renormalization.
Field Theory Model of the Flyby Anomaly
Lewis, R. A
2009-03-16
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.
Field Theory Model of the Flyby Anomaly
NASA Astrophysics Data System (ADS)
Lewis, R. A.
2009-03-01
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.
Incorporation of generalized uncertainty principle into Lifshitz field theories
NASA Astrophysics Data System (ADS)
Faizal, Mir; Majumder, Barun
2015-06-01
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Field theory methods in two-dimensional and heterotic string theories
Morten Ernebjerg
2007-01-01
This thesis has three parts. In the first, we study the Das-Jevicki collective field description of arbitrary classical solutions in the c = 1 matrix model, which are believed to describe nontrivial spacetime backgrounds in 2D string theory. Our analysis naturally includes the case of a Fermi droplet cosmology. We cast the droplet collective field theory in standard coordinates and
Multi-Field Inflation from String Theory
Per Berglund; Guoqin Ren
2009-12-08
We construct a multi-field inflationary model consisting of multiple K\\"ahler moduli derived from type IIB string compactification in the large volume limit. The model consists of both heavy and light fields, with the former being frozen during the inflationary period and the latter acting as the inflaton(s). We study the evolution of all the fields during and after inflation until the preheating era when all the fields oscillate around their vacuum expectation values. Our numerical analysis shows that the curvature perturbations have an almost scale invariant power spectrum with $n_s \\simeq 0.96$.
Heavy Quarks, QCD, and Effective Field Theory
Thomas Mehen
2012-10-09
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.
Topological Field Theory of Time-Reversal Invariant Insulators
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Topological Field Theory of Time-Reversal Invariant Insulators
Xiao-Liang Qi; Taylor Hughes; Shou-Cheng Zhang
2008-02-24
We show that the fundamental time reversal invariant (TRI) insulator exists in 4+1 dimensions, where the effective field theory is described by the 4+1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2+1 dimensions. The TRI quantum spin Hall insulator in 2+1 dimensions and the topological insulator in 3+1 dimension can be obtained as descendants from the fundamental TRI insulator in 4+1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the $Z_2$ topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant $\\alpha=e^2/\\hbar c$. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Non-unitarity in quantum affine Toda theory and perturbed conformal field theory
Gábor Takács; Gérard Watts
1999-01-01
There has been some debate about the validity of quantum affine Toda field theory at imaginary coupling, owing to the non-unitarity of the action, and consequently of its usefulness as a model of perturbed conformal field theory. Drawing on our recent work, we investigate the two simplest affine Toda theories for which this is an issue –a2(1) and a2(2). By
Splitting fields and general differential Galois theory
Trushin, Dmitry V [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2010-11-11
An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions. Bibliography: 14 titles.
New class of effective field theories from embedded branes.
Goon, Garrett L; Hinterbichler, Kurt; Trodden, Mark
2011-06-10
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
Theory of plasma confinement in non-axisymmetric magnetic fields.
Helander, Per
2014-08-01
The theory of plasma confinement by non-axisymmetric magnetic fields is reviewed. Such fields are used to confine fusion plasmas in stellarators, where in contrast to tokamaks and reversed-field pinches the magnetic field generally does not possess any continuous symmetry. The discussion is focussed on magnetohydrodynamic equilibrium conditions, collisionless particle orbits, and the kinetic theory of equilbrium and transport. Each of these topics is fundamentally affected by the absence of symmetry in the magnetic field: the field lines need not trace out nested flux surfaces, the particle orbits may not be confined, and the cross-field transport can be very large. Nevertheless, by tailoring the magnetic field appropriately, well-behaved equilibria with good confinement can be constructed, potentially offering an attractive route to magnetic fusion. In this article, the mathematical apparatus to describe stellarator plasmas is developed from first principles and basic elements underlying confinement optimization are introduced. PMID:25047050
Hadamard subtractions for infrared singularities in quantum field theory
Burton, George Edmund C.
2011-06-27
Feynman graphs in perturbative quantum field theory are replete with infrared divergences caused by the presence of massless particles, how-ever these divergences are known to cancel order-by-order when all virtual and ...