Connection dynamics of a gauge theory of gravity coupled with matter

TL;DR

This paper develops a Hamiltonian formalism for a Poincare gauge theory of gravity coupled with matter, incorporating torsion, and connects it to loop quantum gravity, giving the Barbero-Immirzi parameter a physical interpretation.

Contribution

It provides a complete Hamiltonian analysis of a gravity theory with torsion coupled to matter, leading to a connection formalism suitable for loop quantum gravity quantization.

Findings

Established a SU(2)-connection formalism with torsion

Linked the Barbero-Immirzi parameter to coupling parameters

Enabled loop quantum gravity techniques for this gauge theory

Abstract

We study the coupling of the gravitational action, which is a linear combination of the Hilbert-Palatini term and the quadratic torsion term, to the action of Dirac fermions. The system possesses local Poincare invariance and hence belongs to Poincare gauge theory with matter. The complete Hamiltonian analysis of the theory is carried out without gauge fixing but under certain ansatz on the coupling parameters, which leads to a consistent connection dynamics with second-class constraints and torsion. After performing a partial gauge fixing, all second-class constraints can be solved, and a SU(2)-connection dynamical formalism of the theory can be obtained. Hence, the techniques of loop quantum gravity can be employed to quantize this Poincare gauge theory with non-zero torsion. Moreover, the Barbero-Immirzi parameter in loop quantum gravity acquires its physical meaning as the coupling parameter between the Hilbert-Palatini term and the quadratic torsion term in this gauge theory of gravity.