Hamiltonian formulation of unimodular gravity in the teleparallel geometry

Abstract: In the context of the teleparallel equivalent of general relativity we establish the Hamiltonian formulation of the unimodular theory of gravity. Here we do not carry out the usual $3+1$ decomposition of the field quantities in terms of the lapse and shift functions, as in the ADM formalism. The corresponding Lagrange multiplier is the timelike component of the tetrad field. The dynamics is determined by the Hamiltonian constraint ${\cal H}'_0$ and a set of primary constraints. The constraints are first class and satisfy an algebra that is similar to the algebra of the Poincar\'e group.