Breaking the permutation character of diffeomorphisms on spinor structures

TL;DR

This paper explores how certain diffeomorphisms affect spinor structures on manifolds, revealing a symmetry breaking that influences fermionic modes and their permutation properties.

Contribution

It introduces a novel perspective on the impact of diffeomorphisms on multiple spinor structures, highlighting symmetry breaking in fermionic mode permutations.

Findings

Diffeomorphisms can break symmetry between spinor bundle sections.

Fermionic modes exhibit dynamic preferences influenced by topology.

Permutation symmetry of spinor structures is not always preserved.

Abstract

We investigate the impact of diffeomorphisms where more than one nonequivalent spinor structure is built upon a given base manifold endowed with nontrivial topology. We call attention to the fact that a relatively straightforward construction evinces a lack of symmetry between fermionic modes from different spinor bundle sections, leading to a dynamic preference breaking the permutation character of diffeomorphisms on spinor structures.