Authors apply multisymplectic and polysymplectic formalisms to the known Palatini-Cartan model, recovering torsion-free and Einstein equations, constructing momentum maps and Noether currents, and performing a space-time decomposition into instantaneous Hamiltonian form.
Polysymplectic formulation for BF gravity with Immirzi parameter
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abstract
The polysymplectic formulation of the CMPR action, which is a BF-type formulation of General Relativity that involves an arbitrary Immirzi parameter, is performed. We implement a particular scheme within this covariant Hamiltonian approach to analyze the constraints that characterize the CMPR model. By means of the privileged $(n-1)$-forms and the Poisson-Gerstenhaber bracket, inherent to the polysymplectic framework, the BF field equations associated to the CMPR action are obtained and, in consequence, the Einstein equations naturally emerge by solving the simplicity constraints of the theory. Further, from the polysymplectic analysis of the CMPR action the De Donder-Weyl Hamiltonian formulation of the Holst action is recovered, which is consistent with the Lagrangian analysis of this model as reported in the literature.
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gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Geometric formulation for Palatini-Cartan gravity
Authors apply multisymplectic and polysymplectic formalisms to the known Palatini-Cartan model, recovering torsion-free and Einstein equations, constructing momentum maps and Noether currents, and performing a space-time decomposition into instantaneous Hamiltonian form.