Hamiltonian analysis of General relativity with the Immirzi parameter
Nuno Barros e Sa
TL;DR
This paper conducts a comprehensive Hamiltonian constraint analysis of General relativity with the Immirzi parameter, clarifying the gauge structure and recovering Barbero's formulation in the time gauge.
Contribution
It provides a full constraint analysis for arbitrary Immirzi parameter values and explicitly solves second class constraints, connecting to Barbero's formulation.
Findings
Full Hamiltonian constraint analysis for arbitrary Immirzi parameter
Explicit solution of second class constraints
Recovery of Barbero's formulation in the time gauge
Abstract
Starting from a Lagrangian we perform the full constraint analysis of the Hamiltonian for General relativity in the tetrad-connection formulation for an arbitrary value of the Immirzi parameter and solve the second class constraints, presenting the theory with a Hamiltonian composed of first class constraints which are the generators of the gauge symmetries of the action. In the time gauge we then recover Barbero's formulation of gravity.
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