Canonical description of Pontryagin and Euler classes with a Barbero-Immirzi parameter
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913058127872000 |
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| author | Escalante, Alberto Suárez-Polo, Edmundo Campo, Luis A. Huerta-del |
| author_facet | Escalante, Alberto Suárez-Polo, Edmundo Campo, Luis A. Huerta-del |
| contents | A detailed canonical analysis for Pontryagin and Euler classes with a Barbero-Immirzi [BI] parameter is developed. We rewrite the topological invariants by introducing a set of Holst-like variables, and then study the set of all constraints. We report the complete canonical structure and the symmetries of the theory; we count the physical degrees of freedom and identify reducibility conditions among the constraints. In addition, in our results, if we consider the $BI$ parameter takes the value of $γ= \pm i $, then the self-dual representation of these invariants is reproduced. Finally, we couple the invariants to the Holst action and explore the canonical analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_22400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Canonical description of Pontryagin and Euler classes with a Barbero-Immirzi parameter Escalante, Alberto Suárez-Polo, Edmundo Campo, Luis A. Huerta-del General Relativity and Quantum Cosmology A detailed canonical analysis for Pontryagin and Euler classes with a Barbero-Immirzi [BI] parameter is developed. We rewrite the topological invariants by introducing a set of Holst-like variables, and then study the set of all constraints. We report the complete canonical structure and the symmetries of the theory; we count the physical degrees of freedom and identify reducibility conditions among the constraints. In addition, in our results, if we consider the $BI$ parameter takes the value of $γ= \pm i $, then the self-dual representation of these invariants is reproduced. Finally, we couple the invariants to the Holst action and explore the canonical analysis. |
| title | Canonical description of Pontryagin and Euler classes with a Barbero-Immirzi parameter |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.22400 |