On Hamiltonian formulation of the Einstein-Hilbert action in two dimensions

Abstract

It is shown that the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein-Hilbert action to be a total divergence, if the general covariance is to be preserved, that is, a coordinate system is not fixed. Consequently, a Hamiltonian formulation is possible without any modification of the two dimensional Einstein-Hilbert action. We find the resulting constraints and the corresponding gauge transfromations of the metric tensor.

9 pages

References in corpus (5)

• The Dynamics of General Relativity
• A Canonical Approach to the Einstein-Hilbert Action in Two Spacetime Dimensions
• Energy-Momentum Tensor Improvements in Two Dimensions
• Dirac and Lagrangian reductions in the canonical approach to the first order form of the Einstein-Hilbert action
• Peculiarities of the Canonical Analysis of the First Order Form of the Einstein-Hilbert Action in Two Dimensions in Terms of the Metric Tensor or the Metric Density

Cited by in corpus (12)

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• Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions
• A Canonical Analysis of the Einstein-Hilbert Action in First Order Form
• Perturbative Calculations with the First Order Form of Gauge Theories
• The Canonical Structure of the First Order Einstein-Hilbert Action
• Two-dimensional metric and tetrad gravities as constrained second order systems
• Analysis of Hamiltonian formulations of linearized General Relativity
• General Relativity in two dimensions: a Hamilton-Jacobi constraint analysis
• On the breakdown of space-time in general relativity
• Canonical Formulation of A Bosonic Matter Field in 1+1 Dimensional Curved Space
• Covariant Gauge Fixing and Canonical Quantization
• Algebraic analysis of a model of two-dimensional gravity