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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.00932 |
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| _version_ | 1866918224705093632 |
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| author | Duque, Erick I. |
| author_facet | Duque, Erick I. |
| contents | Fermions are coupled to the Einstein-Cartan system in the canonical formulation, including the cosmological, the Barbero-Immirzi, and the non-minimal coupling constants. The resulting ten first-class constraints generate gauge transformations that are on-shell equivalent to spacetime diffeomorphisms and SL(2,C) transformations. The gravitational second-class constraints receive fermionic contributions, which can be implemented by use of Dirac brackets or by solving them directly. Furthermore, we identify new fermionic (second-class) constraints that are necessary to recover the Dirac-fermion theory by relating the momenta to the configuration variables on dynamical solutions; this fermionic phase-space reduction is accomplished by use of corresponding Dirac brackets. The theory remains well-defined off the second-class constraint surfaces with ten additional degrees of freedom - six of which are gravitational and the remaining four are fermionic. Discrete (CPT) symmetries as well as implications for canonical quantization and modified theories of gravity with fermions are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian gravity with fermions Duque, Erick I. General Relativity and Quantum Cosmology Fermions are coupled to the Einstein-Cartan system in the canonical formulation, including the cosmological, the Barbero-Immirzi, and the non-minimal coupling constants. The resulting ten first-class constraints generate gauge transformations that are on-shell equivalent to spacetime diffeomorphisms and SL(2,C) transformations. The gravitational second-class constraints receive fermionic contributions, which can be implemented by use of Dirac brackets or by solving them directly. Furthermore, we identify new fermionic (second-class) constraints that are necessary to recover the Dirac-fermion theory by relating the momenta to the configuration variables on dynamical solutions; this fermionic phase-space reduction is accomplished by use of corresponding Dirac brackets. The theory remains well-defined off the second-class constraint surfaces with ten additional degrees of freedom - six of which are gravitational and the remaining four are fermionic. Discrete (CPT) symmetries as well as implications for canonical quantization and modified theories of gravity with fermions are discussed. |
| title | Hamiltonian gravity with fermions |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.00932 |