Hamiltonian Analysis of $R + T^2$ Action

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.