Yang–Mills theory and nonirreducible representations of the Lorentz group

1992 ◽  
Vol 70 (5) ◽  
pp. 298-300 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Lorentz Group ◽  
Space Time ◽  
Classical Field ◽  
Field Equations ◽  
Reducible Representation ◽  
Yang Mills ◽  
Special Solutions ◽  
Special Case

We start from an O(4) = SU(2) × SU(2) Yang–Mills theory and argue that the O(4) indices can, in fact, be space-time indices. The resulting theory is that of a tensor, Cμαβ = −Cμβα, which is in a reducible representation of the Lorentz group.fj This is a special case of the extended Yang–Mills formalism of Gabrielli. Some special solutions of the classical field equations are found.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

A gauge theory of the Weyl group

1974 ◽  
Vol 340 (1622) ◽  
pp. 249-262 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conservation Laws ◽  
Weyl Group ◽  
Lorentz Group ◽  
Space Time ◽  
Gauge Fields ◽  
Field Equations ◽  
Covariant Derivatives ◽  
The World

The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincaré group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.

scholarly journals Metric-Affine Gauge Theory of Gravity: I. Fundamental Structure and Field Equations

1997 ◽  
Vol 06 (03) ◽  
pp. 263-303 ◽  
Author(s):  
Frank Gronwald
Keyword(s):  
Gauge Theory ◽  
Reference Frames ◽  
Classical Field Theory ◽  
Classical Field ◽  
Affine Group ◽  
Field Equations ◽  
Yang Mills ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity ◽  
Affine Gravity

We give a self-contained introduction into the metric–affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang–Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric–affine gravity. The results are put into the dynamical framework of a classical field theory. We derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of tranlations is explained in detail.

scholarly journals Axially Symmetric Bulk Viscous String Cosmological Models in GR and Brans-Dicke Theory of Gravitation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
V. U. M. Rao ◽  
D. Neelima
Keyword(s):  
General Relativity ◽  
Bulk Viscosity ◽  
Space Time ◽  
Cosmological Models ◽  
Axially Symmetric ◽  
Matter Distribution ◽  
Field Equations ◽  
Theory Of Gravitation ◽  
The Universe ◽  
Special Case

Axially symmetric string cosmological models with bulk viscosity in Brans-Dicke (1961) and general relativity (GR) have been studied. The field equations have been solved by using the anisotropy feature of the universe in the axially symmetric space-time. Some important features of the models, thus obtained, have been discussed. We noticed that the presence of scalar field does not affect the geometry of the space-time but changes the matter distribution, and as a special case, it is always possible to obtain axially symmetric string cosmological model with bulk viscosity in general relativity.

scholarly journals NONEXISTENCE OF IRREVERSIBLE PROCESSES IN COMPACT SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6227-6241 ◽  
Author(s):  
HOLGER B. NIELSEN ◽  
MASAO NINOMIYA
Keyword(s):  
Compact Space ◽  
Initial Conditions ◽  
Physical Space ◽  
Second Law Of Thermodynamics ◽  
Space Time ◽  
Classical Field ◽  
Irreversible Processes ◽  
Second Law ◽  
Field Equations ◽  
Time Direction

It is shown that if physical space–time were truly compact there would only be of the order-of-one solutions to the classical field equations with a weighting to be explained. But that would not allow any peculiar choice of initial conditions that could support a nontrivial second law of thermodynamics. We present a no-go theorem: irreversible processes would be extremely unlikely to occur for the almost unique solution for the intrinsically compact space–time world, although irreversible processes are well known to occur in general. What we assume here — the compact space–time — is that universe could not exist eternally. In other word if universe stays on forever (i.e. noncompact in time direction) our no-go theorem is not applicable.

scholarly journals Post-Newtonian limit: second-order Jefimenko equations

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
David Pérez Carlos ◽  
Augusto Espinoza ◽  
Andrew Chubykalo
Keyword(s):  
Linear Equations ◽  
Space Time ◽  
Second Order ◽  
Field Equations ◽  
Gravitational Fields ◽  
Mass Distributions ◽  
Minkowski Space Time ◽  
Theory Of Gravitation ◽  
Gravity Probe ◽  
Gravitational Equations

Abstract The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

scholarly journals Flat self-dual gravity

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Kirill Krasnov ◽  
Evgeny Skvortsov
Keyword(s):  
Light Cone ◽  
Space Time ◽  
Kinetic Term ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Covariant Action ◽  
Chiral Interaction ◽  
Double Copy

Abstract We construct a new covariant action for “flat” self-dual gravity in four space-time dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure.

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

scholarly journals ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME

1998 ◽  
Vol 13 (16) ◽  
pp. 2857-2874
Author(s):  
IVER H. BREVIK ◽  
HERNÁN OCAMPO ◽  
SERGEI ODINTSOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Quantum Field ◽  
Curved Space ◽  
Njl Model ◽  
Effective Lagrangian ◽  
Special Solutions ◽  
Curvature Approximation ◽  
Symmetric Phase

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

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