Canonical Lagrangian Dynamics and General Relativity

Details Canonical Lagrangian Dynamics and General Relativity Canonical Lagrangian Dynamics and General Relativity

2008-02-15

arxiv.org/abs/0802.2230v2

Class.Quant.Grav.25:205017,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Version published in Classical and Quantum Gravity. Significant content and references added

Scientific paper

10.1088/0264-9381/25/20/205017

Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizes the role of the Hamiltonian phase space and highlights the role of the Lagrangian phase space. We identify a "Lagrangian one-form" to replace the standard symplectic one-form, which we use to construct the canonical constraints and an associated constraint algebra. The method is particularly useful for generally covariant systems and systems with a degenerate canonical symplectic form, such as Einstein Cartan gravity, to which we apply the method explicitly. We find that one can demonstrate the closure of the constraints without gauge fixing the Lorentz group or introducing primary constraints on the phase space variables. Finally, using geometric quantization techniques, we briefly discuss implications of the formalism for the quantum theory.

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