The Hamilton–Jacobi characteristic equations for three-dimensional Ashtekar gravity
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570, Puebla, Pue., Mexico
2 Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado postal 1152, 72001, Puebla, Pue., Mexico
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Accepted: 3 February 2020
Published online: 12 February 2020
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020