Classification of primary constraints for new general relativity in the premetric approach

TL;DR

This paper develops a new Hamiltonian formalism for new general relativity using the premetric approach, analyzing primary constraints through eigenvalues of the Hessian matrix related to the Lagrangian coefficients.

Contribution

It introduces a novel procedure for classifying primary constraints in NGR based on eigenvalue analysis of the Hessian matrix within the premetric framework.

Findings

Identifies four null eigenvalues linked to trivial primary constraints.

Classifies nine different cases based on eigenvalue vanishing patterns.

Results align with previous Hamiltonian analyses of NGR.

Abstract

We introduce a novel procedure for studying the Hamiltonian formalism of new general relativity (NGR) based on the mathematical properties encoded in the constitutive tensor defined by the premetric approach. We derive the canonical momenta conjugate to the tetrad field and study the eigenvalues of the Hessian tensor, which is mapped to a Hessian matrix with the help of indexation formulas. The properties of the Hessian matrix heavily rely on the possible values of the free coefficients $c_i, i=1,2,3$ appearing in the NGR Lagrangian. We find four null eigenvalues associated with trivial primary constraints in the temporal part of the momenta. The remaining eigenvalues are grouped in four sets, which have multiplicity 3, 1, 5 and 3, and can be set to zero depending on different choices of the coefficients $c_i$. There are nine possible different cases when one, two, or three sets of eigenvalues are imposed to vanish simultaneously. All cases lead to a different number of primary constraints, which are consistent with previous work on the Hamiltonian analysis of NGR by Blixt et al. (2018).