A generalized definition of spin in non-orientable geometries

TL;DR

This paper proposes a new, physically consistent way to define and analyze spin structures in non-orientable geometries, considering their topological effects and multiple possible spin configurations.

Contribution

It introduces a generalized definition of spin in non-orientable spaces and explores the implications of multiple spin structures using cohomological methods.

Findings

Multiple spin structures can exist in non-orientable geometries.

Topological properties influence the energetics of spin configurations.

A generalized framework for spin structures in non-orientable spaces is established.

Abstract

Non-orientable nanostructures are becoming feasable today. This lead us to the study of spin in these geometries. Hence a physically sound definition of spin is suggested. Using our definition, we study the question of the number of different ways to define spin. We argue that the possibility of having more than one spin structure should be taken into account energetically. The effect of topology on spin is studied in detail using cohomological arguments. We generalize the definition of equivalence among (s)pin structures to include non-orientable spaces.