Reflections and spinors on manifolds

TL;DR

This paper reviews recent developments in spin structures and Dirac operators on various manifolds, comparing approaches to spinor fields and analyzing reflection actions, with a focus on spheres, projective spaces, and quadrics.

Contribution

It compares two methods for defining spinor fields on manifolds and discusses reflection symmetries, providing insights into their mathematical properties and applications.

Findings

Comparison of two approaches to spinor fields on manifolds

Analysis of reflection actions on spinors, including chiral spinors

Application to hypersurfaces like spheres and projective spaces

Abstract

This paper reviews some recent work on (s)pin structures and the Dirac operator on hypersurfaces (in particular, on spheres), on real projective spaces and quadrics. Two approaches to spinor fields on manifolds are compared. The action of space and time reflections on spinors is discussed, also for two-component (chiral) spinors.