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arXiv · 1706.06471

On the Hamiltonian formalism of the Tetrad-Gravity with fermions

M. H. Lagraa·M. Lagraa
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Abstract

We extend the analysis of the Hamiltonian formalism of the d-dimensional tetrad-connection gravity to the fermionic field by fixing the non-dynamic part of the spatial connection to zero. Although the reduced phase space is equipped with complicated Dirac brackets, the first-class constraints which generate the diffeomorphisms and the Lorentz transformations satisfy a closed algebra with structural constants analogous to that of the pure gravity. We also show the existence of a canonical transformation leading to a new reduced phase space equipped with Dirac brackets having a canonical form leading to the same algebra of the first-class constraints.

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M. H. Lagraa, M. Lagraa. 2017-06-19. On the Hamiltonian formalism of the Tetrad-Gravity with fermions. https://doi.org/10.1007/s10714-018-2386-0

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