Hamiltonian Poincaré Gauge Theory of Gravitation

Abstract

We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincaré group, taken as the local spacetime group of the gravitational gauge theory, with $SO(3)$ as the classification subgroup. The Wigner--like rotation induced by the nonlinear approach singularizes out the role of time and allows to deal with ordinary $SO(3)$ vectors. We apply the general results to the Einstein--Cartan action. We study the constraints and we obtain Einstein's classical equations in the extremely simple form of time evolution equations of the coframe. As a consequence of our approach, we identify the gauge--theoretical origin of the Ashtekar variables.

38 pages, plainTeX

References in corpus (4)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Avoiding degenerate coframes in an affine gauge approach to quantum gravity
• Ordinary Matter in Nonlinear Affine Gauge Theories of Gravitation

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• A perturbation approach to Translational Gravity