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arXiv · 2512.22400

Canonical description of Pontryagin and Euler classes with a Barbero-Immirzi parameter

Alberto Escalante·Edmundo Suárez-Polo·Luis A. Huerta-del Campo
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Abstract

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 $\gamma = \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.

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Alberto Escalante, Edmundo Suárez-Polo, Luis A. Huerta-del Campo. 2025-12-26. Canonical description of Pontryagin and Euler classes with a Barbero-Immirzi parameter. https://arxiv.org/abs/2512.22400

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