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On the Hamiltonian formalism of the tetrad-gravity with fermions

  • M. H. Lagraa
  • M. Lagraa
Research Article

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 (Lagraa et al. in Class Quantum Gravity 34:115010, 2017). 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.

Keywords

Tetrad-connection gravity Hamiltonian formalism Dirac spinors Dirac brackets 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.École supérieure en Génie Électrique et Énergétique d’Oran (ESG2E) (Ex-EPSTO)OranAlgeria
  2. 2.Laboratoire de physique théorique d’Oran (LPTO)Université d’Oran I, Ahmed BenbellaOranAlgeria

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