Hamiltonian formulation of general relativity in the teleparallel geometry

We establish a Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing a Legendre transform. The time gauge condition, previously considered, restricts the teleparallel geometry to the three-dimensional spacelike hypersurface. Geometrically, the teleparallel geometry is now extended to four-dimensional space-time. The resulting Hamiltonian formulation is structurally different from the standard Arnowitt-Deser-Misner formulation in many aspects, the main one being that the dynamics is now governed by the Hamiltonian constraint H₀ and a set of primary constraints. The vector constraint H₈ is derived from the Hamiltonian constraint. The vanishing of the latter implies the vanishing of the vector constraint.