Hamiltonian Analysis of $R + T^2$ Action

TL;DR

This paper performs a detailed Hamiltonian analysis of a Poincare-invariant gravitational action combining the Hilbert-Palatini term with a quadratic torsion term, revealing new constraints and structures despite identical equations of motion to General Relativity.

Contribution

It uncovers novel aspects of the Hamiltonian structure of torsion-inclusive gravity actions without gauge fixing, extending the understanding of constraints in such theories.

Findings

Additional torsion term in the spatial diffeomorphism constraint

Primary second-class constraints require a different imposition method

Results offer insights into Hamiltonian systems with torsion

Abstract

We study a gravitational action which is a linear combination of the Hilbert-Palatini term and a term quadratic in torsion and possessing local Poincare invariance. Although this action yields the same equations of motion as General Relativity, the detailed Hamiltonian analysis without gauge fixing reveals some new points never shown in the Hilbert-Palatini formalism. These include that an additional term containing torsion appears in the spatial diffeomorphism constraint and that the primary second-class constraints have to be imposed in a manner different from that in the Hilbert-Palatini case. These results may provide valuable lessons for further study of Hamiltonian systems with torsion.