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

Understand

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.