General Relativity in two dimensions: a Hamilton-Jacobi constraint analysis
M.C.Bertin, B.M.Pimentel, P.J.Pompeia
TL;DR
This paper applies the Hamilton-Jacobi method to analyze the constraint structure of two-dimensional General Relativity, identifying involutive and non-involutive constraints and demonstrating how to ensure integrability and derive field equations.
Contribution
It introduces a Hamilton-Jacobi framework for understanding the constraint structure in 2D General Relativity, including the use of generalized brackets for constraint management.
Findings
Identified involutive and non-involutive constraints in 2D GR
Demonstrated the use of generalized brackets to ensure integrability
Derived the field equations from the constraint analysis
Abstract
We will analyze the constraint structure of the Einstein-Hilbert first-order action in two dimensions using the Hamilton-Jacobi approach. We will be able to find a set of involutive, as well as a set of non-involutive constraints. Using generalized brackets we will show how to assure integrability of the theory, to eliminate the set of non-involutive constraints, and to build the field equations.
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