Topological parameters in gravity

TL;DR

This paper analyzes a gravity theory incorporating topological densities, revealing a modified symplectic structure and a real SU(2) gauge description with parameters influencing the canonical formulation.

Contribution

It provides a Hamiltonian analysis of gravity with topological terms, introducing a dependence on three parameters and deriving a real SU(2) gauge theory formulation.

Findings

The symplectic structure is non-trivially modified by topological terms.

The theory develops a parameter-dependent canonical structure.

The Barbero-Immirzi parameter emerges as a coupling constant.

Abstract

We present the Hamiltonian analysis of the theory of gravity based on a Lagrangian density containing Hilbert-Palatini term along with three topological densities, Nieh-Yan, Pontryagin and Euler. The addition of these topological terms modifies the symplectic structure non-trivially. The resulting canonical theory develops a dependence on three parameters which are coefficients of these terms. In the time gauge, we obtain a real SU (2) gauge theoretic description with a set of seven first class constraints corresponding to three SU (2) rotations, three spatial diffeomorphism and one to evolution in a timelike direction. Inverse of the coefficient of Nieh-Yan term, identified as Barbero-Immirzi parameter, acts as the coupling constant of the gauge theory.