The Hamilton-Jacobi characteristic equations for three dimensional Ashtekar gravity

2020/02/11 by Alberto Escalante, Escalante, Alberto, M. Eduardo Hernández-García +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.2002.11769

arxiv created 2020/02/11 · arxiv updated 2020/02/28

Abstract

The Hamilton-Jacobi analysis of three dimensional gravity defined in terms of Ashtekar-like variables is performed. We report a detailed analysis where the complete set of Hamilton-Jacobi constraints, the characteristic equations and the gauge transformations of the theory are found. We find from integrability conditions on the Hamilton-Jacobi Hamiltonians that the theory is reduced to a BF field theory defined only in terms of self-dual (or anti-self-dual) variables; we identify the dynamical variables and the counting of physical degrees of freedom is performed. In addition, we compare our results with those reported by using the canonical formalism.

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