The Canonical Structure of the First Order Einstein-Hilbert Action

Abstract

The Dirac constraint formalism is used to analyze the first order form of the Einstein-Hilbert action in d > 2 dimensions. Unlike previous treatments, this is done without eliminating fields at the outset by solving equations of motion that are independent of time derivatives when they correspond to first class constraints. As anticipated by the way in which the affine connection transforms under a diffeomorphism, not only primary and secondary but also tertiary first class constraints arise. These leave d(d - 3) degrees of freedom in phase space. The gauge invariance of the action is discussed, with special attention being paid to the gauge generators of Henneaux, Teitelboim and Zanelli and of Castellani.

References in corpus (5)

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• Diffeomorphism Symmetry in the Lagrangian Formulation of Gravity
• Two-dimensional metric and tetrad gravities as constrained second order systems
• Canonical Formulation of A Bosonic Matter Field in 1+1 Dimensional Curved Space

Cited by in corpus (16)

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• On the breakdown of space-time in general relativity
• Use of Lagrange multiplier fields to eliminate multiloop corrections
• Generators of Local Supersymmetry Transformation from First Class Constraints
• Symplectic Analysis of the Two Dimensional Palatini Action
• Quantizing the Palatini action using a transverse traceless propagator
• Covariant Gauge Fixing and Canonical Quantization
• The Canonical Structure of the First Order Einstein-Hilbert Action with a Flat Background
• Equivalence of first and second order formulations of the Einstein-Hilbert theory
• Treatment of a System with Explicitly Broken Gauge Symmetries
• Covariant quantization of the Einstein-Hilbert theory in first-order form