Gauge Theory Of Gravity Research Articles

On the renormalizability of a gauge theory of gravitation

One-loop divergences in gauge theory of gravitation with a quadratic Lagrangian are computed. The renormalizability of the theory in the case of Riemannian background is shown.

Spherically Symmetric and Static Fields in Linearized Gauge Theories of Gravitation

In this paper Newtonian limit in the Poincare gauge field theory of gravitation is investigated. In spherically symmetric and static cases interior and exterior solutions of the linearized field equations with gravitational source are obtained by maens of Green's function for the five Lagrangians without ghosts and tachyons. In cases of four Lagrangians, the space-time metrics outside gravitational source are the usual Schwarzschild one of the first-order, while in the case of the fifth Lagrangian the space-time metric differs from the Schwarzschild one. Under both, Newtonian and weak gravitational field approximations, the motion of a test particle without spin should therefore be different from Newton's second law. As a result of the exchanged particles of spin the deviation from Newton's second law is a Yukawa term which is attractive. A distance-dependent gravitational “constant” G(r) can be defined according to the new result. The difference between G(r) and Newton's gravitational constant is due to a nonzero component of torsion tensor, the effect of which can be tested by measuring G(r).

Cosmological term in the general theory of relativity and localization of the de Sitter and Einstein groups

The theory of a gauge gravitational field with localization of the de Sitter group is formulated. Starting from the tetradic components of the de Sitter universe, a relationship is established between the Riemannian metric and the de Sitter gauge field. It is shown that the general theory of relativity with the cosmological term is the simplest variant of the de Sitter gauge theory of gravitation, which transforms in the limit of an infinite radius of curvature of the de Sitter universe into the Poincare-invariant GTR without the cosmological term. A theory of a gauge gravitational field with localization of Einstein's group of motions of the uniform static universe (the Einstein group R × S0 (4)) is formulated in an analogous manner.

Spontaneous compactification in a six-dimensional Poincaré gauge field theory of gravitation

We found a solution for the torsion tensor in a six-dimensional Poincaré gauge theory of gravitation. This torsion tensor supports a Riemann-Cartan geometry which is the product of a minkowskian four-space and a two-sphere whose radius is determined by the field equations to be of the order of the Planck length. This solution exists when there are some restrictions on the parameters of the lagrangian of the theory.

Reduction of the Poincaré gauge field equations by means of duality rotations

A rather general procedure is developed in order to reduce the two field equations of the Poincaré gauge theory of gravity by a modified ansatz for the curvature tensor involving double duality. In the case of quasilinear Lagrangians of the Yang–Mills type it is shown that nontrivial torsion solutions with duality properties necessarily ‘‘live’’ on an Einstein space as metrical background.

On the significance of the compatibility condition in gauge theories of the Poincare group

A fundamental mathematical distinction between the Lorentz and Poincare groups is shown to have important consequences for the status of the compatibility condition ( Del g=0) in gauge theories of gravitation.

On pseudoparticle solutions in the poincaré gauge theory of gravity

AbstractThe dynamical structure of the Poincaré gauge field theory coupled to matter fields and some of its implications for a quantum theory of gravity are investigated.Essentially, the method of BELAVIN et al. for generating instanton solutions in Yang‐Mills theory is transferred to the gravitational gauge model. The result are as follows: For configurations obeying a modified double duality Ansatz for the curvature the metrical background is determined by Einstein‐type field equations coupled almost canonically to the stress‐energy content of external fields.Exact electrovac solutions with non‐trivial torsion are derived from the duality Ansatz. In a Euclidean space‐time the corresponding pseudoparticle solutions are expected to play a dominant rǒle in the quantization of gravity via Freynman's method of path integrals.

On the Definition of Gauge Transformations in Gauge Theory

AbstractThe different types of gauge transformations in gauge theory are discerned and defined in fiber bundle terms. The gauge gravitation case is analysed in order to examine various versions of the gauge gravitation theory.

Hamiltonian dynamics of Poincaré gauge theory: General structure in the time gauge

General aspects of the Hamiltonian structure of Poincar\'e gauge theory of gravity with $R+{T}^{2}+{R}^{2}$ type of Lagrangian are investigated in the time gauge. The explicit form of the Hamiltonian is found, taking care of the fact that some of the primary constraints exist only if some specific relations among the constants of the theory are satisfied. The consistency conditions of the primary constraints are obtained, and their dynamical meaning is clarified in the case corresponding to the existence of massive tordions in the weak-field approximation of the theory. The way to construct the Dirac brackets is indicated.

Plane-fronted torsion waves in a gravitational gauge theory with a quadratic Lagrangian

We find plane-fronted torsion waves propagating in the metrically flat spacetime in a gravitational gauge theory formulated in a Riemann-Cartan spacetime with Lagrangian ${R}_{\mathrm{ij}}{R}^{\mathrm{ij}}\ensuremath{-}\frac{1}{3}{R}^{2}$.

How to fix the gauge in internal and external gauge theories

A recently presented method, that permits one to calculate gauge-fixing conditions from a given gauge-breaking term, is applied to internal as well as external Yang-Mills theories. As to the internal case, the known gauge-fixing conditions can easily be reproduced in a unified way. For the external case, i.e., the Poincare gauge theory of gravitation, new gauge-fixing conditions are obtained, in particular the full nonlinear generalization of the Coulomb and axial gauge. They prove to be simultaneously valid for theories with or without torsion.

Field equations of the gauge theory of gravitation originate from a quadratic Lagrangian with torsion

The equations of the gauge theory of gravitation [Debney et al.General Relativity and Gravitation,9, 879–887 (1978)] are derived from a complex quadratic Lagrangian with torsion. The derivation is performed in a coordinate basis in a completely covariant way.

Dirac gravitational magnetic monopoles do not exist

We show that the gravitational analog of the Dirac magnetic monopole does not exist for a gauge theory of gravitation with either a T4 or an SL(2, C) × T4 gauge group.

Gauge theory of gravity

We develop an O(5) gauge theory in which the O(5) symmetry is spontaneously broken to O(4) with a scale on the order of the Planck mass. The ten components of the O(5) gauge field are identified as the four vierbeins and six connections of Euclidean general relativity. In the strong-coupling limit the effective action is dominated by a dimension-five operator induced by the anomalous fermion triangle loop which turns out to be the usual Hilbert action. The metric is not a dynamical field in this model and its equation of constraint is just the usual metric-vierbein relation. We suggest SU(9) \ensuremath{\supset} SU(5)\ifmmode\times\else\texttimes\fi{}O(5) as the simplest group for a totally unified theory.

On the Exterior Solutions of a Charged Mass Point in Gauge Theories of Gravitation

In a case of spherically symmetric and static field, exterior solutions of a charged mass point for the nine-parameter gravitational theories are investigated. We obtain results as follows: in the case of coupling constant , solution without torsion is the Reissner-Nordstrom metric; otherwise there is no solution with vanishing torsion.

Generalised cosmological Friedmann equations and the de Sitter solution

It is shown that the generalised cosmological Friedmann equations in the gauge theory of gravitation obtained earlier have solutions with the de Sitter metric and vanishing as well as nonvanishing torsion.

Hamiltonian formulation of the gauge theory of gravitation. Pure-gravity case

The gauge theory of gravitation invariant underO 5 and the general co-ordinate transformations is formulated by using Dirac’s Hamiltonian formalism. The tetrad field is introduced as a connection of theO 5 gauge group. By fixing the boost part of this gauge freedom, the spin connection is eliminated by using second-class constraints. As a result the system is described by the tetrad field with a set of first-class constraints associated to the local Lorentz and the general co-ordinate transformations.

Dynamical effect of torsion in gravitaional field

In this paper we discuss the dynamical properties of a spinning body in a gravitational gauge theory containing torsion. Formulae are given for the precession of the Earth in the static spherically-symmetric field of the Sun and of the gyroscope. These formulae are valid for any model of gauge theory that includes torsion.

Hamiltonian formulation for a translation gauge theory of gravitation

Dirac’s Hamiltonian methods are applied to a gauge theory of the translation group formulated by Hayashi as a gravitational theory which stands on microscopical scale. Four constraint equations are obtained, as in general relativity, because of the existence of the spacetime translation group, which is a group of invariance of the theory. Propagation equations for the dynamical variables are also derived.

Nonsymmetric gauge theory of gravitation

In this paper we give a nonsymmetric unified field theory, i.e., a gravitational gauge theory in which we take the group U(3,1) \ensuremath{\bigotimes} SU(2) as the gauge group. The electromagnetic field and the Yang-Mills field are brought naturally into the geometric construction of the spacetime. According to this theory, the torsion, which is Hermitian antisymmetric and its every component is a 2\ifmmode\times\else\texttimes\fi{}2 complex matrix, exists in the spacetime. In the special case or limit case, the U(3,1) gravitational gauge theory, the Lorentz gravitational gauge theory, the Einstein-Moffat-Boal theory, the Einstein-Maxwell theory, and general relativity are included in our theory.