Geometrodynamics vs. Connection Dynamics

Details Geometrodynamics vs. Connection Dynamics Geometrodynamics vs. Connection Dynamics

1993-03-26

arxiv.org/abs/gr-qc/9303032v1

Gen.Rel.Grav. 25 (1993) 759-854

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

88 pages (Latex file), UMDGR-93-129

Scientific paper

10.1007/BF00758384

The purpose of this review is to describe in some detail the mathematical relationship between geometrodynamics and connection dynamics in the context of the classical theories of 2+1 and 3+1 gravity. I analyze the standard Einstein-Hilbert theory (in any spacetime dimension), the Palatini and Chern-Simons theories in 2+1 dimensions, and the Palatini and self-dual theories in 3+1 dimensions. I also couple various matter fields to these theories and briefly describe a pure spin-connection formulation of 3+1 gravity. I derive the Euler-Lagrange equations of motion from an action principle and perform a Legendre transform to obtain a Hamiltonian formulation of each theory. Since constraints are present in all these theories, I construct constraint functions and analyze their Poisson bracket algebra. I demonstrate, whenever possible, equivalences between the theories.

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