Gravitational Goldstone fields from affine gauge theory

Abstract

In order to facilitate the application of standard renormalization techniques, gravitation should be decribed, if possible, in pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincare or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring the "hidden" piece responsible for this behavior within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide a general mathematical scheme clarifying the foundations of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the affine group, tetrads become identified with nonlinear translational connections; the anholonomic metric does not constitute any more an independent gravitational potential, since its degrees of freedom reveal to correspond to eliminable Goldstone bosons. This may be an important advantage for quantization.

LaTeX, 9 pages, no figures. Revised version, slightly differing from the published one in a few presentation details

References in corpus (4)

• Dynamical measure and field theory models free of the cosmological constant problem
• Comment on: Topological Invariants, instantons, and the chiral anomaly on spaces with torsion
• Scale Invariance and Vacuum Energy
• Scale Symmetry Spontaneously Broken by Asymptotic Behavior

Cited by in corpus (39)

• The spectrum of symmetric teleparallel gravity
• A Higgs Mechanism for Gravity
• Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity
• The Higgs sector of gravitational gauge theories
• Canonical and gravitational stress-energy tensors
• On an integrable geometrical foundation of gravity
• Elie Cartan's torsion in geometry and in field theory, an essay
• The Nontriviality of Trivial General Covariance: How Electrons Restrict 'Time' Coordinates, Spinors (Almost) Fit into Tensor Calculus, and 7/16 of a Tetrad Is Surplus Structure
• On the teleparallel limit of Poincare gauge theory
• An axiomatic purification of gravity
• Dynamically broken Anti-de Sitter action for gravity
• Deriving the mass of particles from Extended Theories of Gravity in LHC era
• On the topological reduction from the affine to the orthogonal gauge theory of gravity
• Translations and dynamics
• de Sitter group and Einstein-Hilbert Lagrangian
• Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation
• A review about Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry
• Einsteinian gravity from a topological action
• $D=4$ topological gravity from gauging the Maxwell-special-affine group
• Maxwell-affine gauge theory of gravity
• Anomalies and gravity
• Nonlinear Realization of the Local Conform-Affine Symmetry Group for Gravity in the Composite Fiber Bundle Formalism
• Gravitational contribution to fermion masses
• The Affine Structure of Gravitational Theories: Symplectic Groups and Geometry
• On the difference between Poincaré and Lorentz gravity
• Classical r-matrices for the generalised Chern-Simons formulation of 3d gravity
• Higgs and Goldstone modes in crystalline solids
• A new attempt towards the unification of space-time and internal gauge symmetries
• Discrete Gravity as a Local Theory of the Poincaré Group in the First Order Formalism
• The role of translational invariance in non linear gauge theories of gravity
• One-parameter teleparallel limit of Poincare gravity
• An assessment of Evans' unified field theory I
• Motion in gauge theories of gravity
• Tangent space symmetries in general relativity and teleparallelism
• Maxwell-Modified Metric Affine Gravity
• A Higgs--Chern-Simons gravity model in 2+1 dimensions
• Cosmological Constant, Inflaton, and Dark Matter all Naturally Originated from Poincaré Gauge Gravity
• Background-Independence from the Perspective of Gauge Theory
• A proposal of foundation of spacetime geometry