Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation

Abstract

According to Yang \& Mills (1954), a {\it conserved} current and a related rigid (`global') symmetry lie at the foundations of gauge theory. When the rigid symmetry is extended to a {\it local} one, a so-called gauge symmetry, a new interaction emerges as gauge potential $A$; its field strength is $F\sim \mathrm{curl}A$. In gravity, the conservation of the energy-momentum current of matter and the rigid translation symmetry in the Minkowski space of special relativity lie at the foundations of a gravitational gauge theory. If the translation invariance is made local, a gravitational potential $\vartheta$ arises together with its field strength $T\sim \mathrm{curl}\vartheta$. Thereby the Minkowski space deforms into a Weitzenböck space with nonvanishing torsion $T$ but vanishing curvature. The corresponding theory is reviewed and its equivalence to general relativity pointed out. Since translations form a subgroup of the Poincaré group, the group of motion of special relativity, one ought to straightforwardly extend the gauging of the translations to the gauging of full Poincaré group thereby also including the conservation law of the {\it angular momentum} current. The emerging Poincaré gauge (theory of) gravity, starting from the viable Einstein-Cartan theory of 1961, will be shortly reviewed and its prospects for further developments assessed.

arXiv comment46 pages, 4 figures, minor corrections, references added, contribution to "One Hundred Years of Gauge Theory" edited by S. De Bianchi and C. Kiefer

References in corpus (53)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Physical Aspects of the Space-Time Torsion
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Phase shift in atom interferometry due to spacetime curvature
• Metric-affine approach to teleparallel gravity
• Gravitoelectromagnetism: A Brief Review
• Effective inertial frame in an atom interferometric test of the equivalence principle
• Nonlocal Gravity Simulates Dark Matter
• Beyond Einstein-Cartan gravity: Quadratic torsion and curvature invariants with even and odd parity including all boundary terms
• A formal framework for a nonlocal generalization of Einstein's theory of gravitation
• Cosmology with a spin
• Friedmann-like universes with torsion
• Status of non-Riemannian cosmology
• On Poincaré gauge theory of gravity, its equations of motion, and Gravity Probe B
• Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part
• Nonlocal Modification of Newtonian Gravity
• Big bounce from spin and torsion
• Gauge Structure of Teleparallel Gravity
• Cosmological dynamics with propagating Lorentz connection modes of spin zero
• Normal frames for non-Riemannian connections
• General Poincaré gauge theory: Hamiltonian structure and particle spectrum
• Schwarzschild and Kerr Solutions of Einstein's Field Equation -- an introduction
• Low-energy general relativity with torsion: a systematic derivative expansion
• Energy-momentum current for coframe gravity
• The particle spectrum of parity-violating Poincaré gravitational theory
• New torsion black hole solutions in Poincaré gauge theory
• On the spin-rotation-gravity coupling
• Infrared Modified Gravity with Dynamical Torsion
• On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics
• Canonical Transformation Path to Gauge Theories of Gravity
• Elie Cartan's torsion in geometry and in field theory, an essay
• Extended Reissner-Nordström solutions sourced by dynamical torsion
• Premetric equivalent of general relativity: Teleparallelism
• Normal frames and the validity of the equivalence principle
• Exact Solutions in Poincaré Gauge Gravity Theory
• Premetric teleparallel theory of gravity and its local and linear constitutive law
• The General Linear Cartan Khronon
• Poincaré Gauge Theory With Coupled Even And Odd Parity Dynamic Spin-0 Modes: Dynamic Equations For Isotropic Bianchi Cosmologies
• Spin - Rotation Coupling Observed in Neutron Interferometry
• Translations and dynamics
• Entropy in Poincaré gauge theory: Hamiltonian approach
• Multipolar test body equations of motion in generalized gravity theories
• Constitutive law of nonlocal gravity
• Infrared modified gravity with propagating torsion: instability of torsionfull de Sitter-like solutions
• Self-accelerating Universe in modified gravity with dynamical torsion
• Torsional Topological Invariants
• Late-time acceleration and inflation in a Poincaré gauge cosmological model
• Spherically symmetric solutions in torsion bigravity
• Hamiltonian approach to black hole entropy: Kerr-like spacetimes
• Torsion in Gauge Theory
• Generic Theory of Geometrodynamics from Noether's theorem for the Diff(M) symmetry group
• Poincare gauge gravity: selected topics
• A Theory of Gravitation Covariant under $Sp(4,\mathbf{R})$}

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• New effective theories of gravitation and their phenomenological consequences