On the Hamiltonian formalism of the tetrad-connection gravity

摘要

We present a detailed analysis of the Hamiltonian constraints of the d-dimensional tetrad-connection gravity where the non-dynamic part of the spatial connection is fixed to zero by an adequate gauge transformation. This new action leads to a coherent Hamiltonian formalism where the Lorentz, scalar and vectorial first-class constraints obey a closed algebra in terms of Poisson brackets. This algebra closes with structure constants instead of structure functions resulting from the Hamiltonian formalisms based on the A.D.M. decomposition. The same algebra of the reduced first-class constraints, where the second-class constraints are eliminated as strong equalities, is obtained in terms of Dirac brackets. These first-class constraints lead to the same physical degrees of freedom of the general relativity.