Hamiltonian and primary constraints of new general relativity

Understand

We derive the kinematic Hamiltonian for the so-called "new general relativity" class of teleparallel gravity theories, which is the most general class of theories whose Lagrangian is quadratic in the torsion tensor and does not contain parity violating terms.

• Our approach makes use of an explicit expression for the flat, in general, nonvanishing spin connection, which avoids the use of Lagrange multipliers, while keeping the theory invariant under local Lorentz transformations.
• We clarify the relation between the dynamics of the spin connection degrees of freedom and the tetrads.
• The terms constituting the Hamiltonian of the theory can be decomposed into irreducible parts under the rotation group.