General relativity as a gauge theory of the Poincaré group, the symmetric momentum tensor of both matter and gravity, and gauge-fixing conditions

Abstract

It is shown that a consistent gauging of the Poincare group is capable of including Einstein's general relativity. This statement holds for matter particles of arbitrary spin, provided the nontrivial part of the vierbein is taken as the fundamental gravitational field, thus giving rise to a known modification of the original theory. Since the gauge approach implies that gravitation is an ordinary field theory over flat space, the standard prescriptions for calculating the asymmetric momentum tensor of both matter and gravitation are available. Applying Belinfante's flat-space symmetrization procedure to the latter, we prove that the symmetrization of the asymmetric matter tensor just gives the dynamically defined symmetric matter tensor, whereas the symmetrization of the asymmetric gravitational momentum tensor leads to another version of the field equations that reveals a deep analogy to the equations of electrodynamics. Furthermore a method is developed that admits an unambiguous calculation of gauge-fixing conditions from a given gauge-breaking term. Besides the harmonic gauge, which can be reproduced by means of this method, new gauge-fixing conditions for local translations and local Lorentz transformations are obtained. These gaugefixing techniques, as well as the symmetrization procedure, may equally be generalized to the case of nonvanishing torsion.-

A Riccati type PDE for light-front higher helicity vertices

“…Similar results hold for interacting spin 2 fields, eventually leading to the full Einstein theory as investigated by many authors [66][67][68][69][70][71][72][73][74][75] and generalized to supergravity theories [76,77]. The source of this deformation theoretic approach to interacting gauge field theories can be traced back to Gupta's work on gravity in [78,79] as pointed out by Fang and Fronsdal in [80] -a paper that can be seen as the genesis of deformation approaches to higher spin gauge field interactions.…”

The Hamiltonian formulation of tetrad gravity: Three-dimensional case

“…These constraints, (14), are not of a special form [3], but they are linear in ω p(q0) and Π p(q0) and the coefficient in front of ω p(q0) in (14) does not depend either on…”

Higgs and Goldstone Modes in Crystalline Solids

“…The correct understanding of was given by Y. M. Cho, who developed a gauge theory of translations with a Yang–Mills–type Lagrangian, where the gauge potentials were correctly interpreted as translational connections (in particular, they are the nontrivial part of the vierbein fields ), and not as general coordinate transformations on the base manifold (as e.g., in Utiyama), that would have been not correct. D. and G. Grensing came to similar conclusions, obtaining the gauging of the Poincaré group in a form that allowed to express General Relativity as a gauge theory of this symmetry group. More recently, the Yang–Mills theory of the affine group (the semidirect product of translations and general linear transformations ) was formulated, where tetrads have been identified with nonlinear translational connections, for which the given expression is a simplified yet correct version of the general formulation.…”

“…In fact, it turns out that the acoustic phonon travels in the crystal acting as a wavelike perturbation of the lattice, similarly to the graviton in vacuum, that travels as a wavelike perturbation of a locally flat differentiable manifold, both obeying very similar field equations. [25][26][27][28][29][30] Acoustic phonons arise in this case not as Goldstone, but as gauge bosons.…”