We present Hamilton’s equations for the teleparallel equivalent of general
relativity (TEGR), which is a reformulation of general relativity based on a
curvatureless, metric compatible, and torsionful connection. For this, we
consider the Hamiltonian for TEGR obtained through the vector, antisymmetric,
symmetric and trace-free, and trace irreducible decomposition of the phase
space variables. We present the Hamiltonian for TEGR in the covariant formalism
for the first time in the literature, by considering a spin connection
depending on Lorentz matrices. We introduce the mathematical formalism
necessary to compute Hamilton’s equations in both Weitzenbock gauge and
covariant formulation, where for the latter we must introduce new fields:
Lorentz matrices and their associated momenta. We also derive explicit
relations between the conjugate momenta of the tetrad and the conjugate momenta
for the metric that are traditionally defined in GR, which are important to
compare both formalisms.
