Deformations in spinor bundles: Lorentz violation and further physical implications
J. M. Hoff da Silva, R. T. Cavalcanti, G. M. Caires da Rocha
TL;DR
This work investigates how nontrivial topology induces deformations in spinor bundles, introducing a real deformation function $\varphi(x)$ that modulates spinor transition maps and causes Lorentz and Poincaré symmetry violations in regionally distinct ways. It develops a rigorous mathematical framework for spinor-structure deformations, including a covariant derivative $\nabla_\mu$ enriched by $\varphi(x)$ and a cohomological analysis of spinor-structure equivalence via a $\Gamma$-structure and the group $\check{H}^1(\mathcal{M},\mathbb{Z}_2)$. The paper then derives physical consequences: a junction condition for current conservation at region boundaries, quasinormal-like behavior and a modified Gordon decomposition yielding an effective magnetic moment for exotic spinors, and a geometrized nonlinear sigma model on a deformed metric, illustrating how topology-induced deformations influence dynamics and observable quantities. Overall, it provides a robust mathematical-numerical toolkit for exploring exotic spinor behavior in curved/spacetime with nontrivial topology, with potential implications for high-energy phenomenology and topological effects in Lorentz-violating scenarios.
Abstract
This paper delves into the deformation of spinor structures within nontrivial topologies and their physical implications. The deformation is modeled by introducing real functions that modify the standard spinor dynamics, leading to distinct physical regions characterized by varying degrees of Lorentz symmetry violation. It allows us to investigate the effects in the dynamical equation and a geometrized nonlinear sigma model. The findings suggest significant implications for the spinor fields in regions with nontrivial topologies, providing a robust mathematical approach to studying exotic spinor behavior.