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On the Hamiltonian formalism of the tetrad-gravity with fermions. (English) Zbl 1392.83076
Summary: 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 [the first author et al., Classical Quantum Gravity 34, No. 11, Article ID 115010, 25 p. (2017; Zbl 1370.83081)]. 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.
MSC:
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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