Hamiltonian Poincaré Gauge Theory of Gravitation

Details Hamiltonian Poincaré Gauge Theory of Gravitation Hamiltonian Poincaré Gauge Theory of Gravitation

1996-03-15

arxiv.org/abs/gr-qc/9603023v1

Class.Quant.Grav. 14 (1997) 549-575

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

38 pages, plainTeX

Scientific paper

10.1088/0264-9381/14/2/027

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 Poincar\'e 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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