Three-dimensional Background Field Gravity: A Hamilton-Jacobi analysis
N. T. Maia, B. M. Pimentel, C. E. Valc\'arcel
TL;DR
This paper analyzes the constraint structure of a three-dimensional gravity model with a background field and cosmological term using Hamilton-Jacobi formalism, identifying involutive Hamiltonians and gauge generators.
Contribution
It provides a detailed Hamilton-Jacobi analysis of the 3D background field gravity model, establishing its integrability and gauge structure.
Findings
Identified the complete set of involutive Hamiltonians.
Established the equivalence between characteristic equations and field equations.
Derived generators of canonical and gauge transformations.
Abstract
We analyse the constraint structure of the Background Field model for three dimensional gravity including a cosmological term via the Hamilton-Jacobi formalism. We find the complete set of involutive Hamiltonians that assures the integrability of the system and calculate the characteristic equations of the system. We established the equivalence between these equations and the field equations and also obtain the generators of canonical and gauge transformations.
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