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Hamiltonian Poincaré Gauge Theory of Gravitation

A. López--Pinto·A. Tiemblo·R. Tresguerres
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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.

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A. López--Pinto, A. Tiemblo, R. Tresguerres. 1996-03-15. Hamiltonian Poincaré Gauge Theory of Gravitation. https://doi.org/10.1088/0264-9381%2F14%2F2%2F027

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