Generalized Dirac operators on Lorentzian manifolds and propagation of singularities

TL;DR

This paper reviews the proper definition of generalized Dirac operators on Lorentzian manifolds and confirms that singularities propagate along light-like geodesics, extending classical results to these operators.

Contribution

It establishes that the propagation of singularities along light-like geodesics holds for generalized Dirac operators on Lorentzian manifolds, confirming a key classical property.

Findings

Propagation of singularities along light-like geodesics confirmed for generalized Dirac operators

Correct definition of generalized Dirac operators on Lorentzian manifolds provided

Classical propagation results extended to a broader class of operators

Abstract

We survey the correct definition of a generalized Dirac operator on a Space--Time and the classical result about propagation of singularities. This says that light travels along light--like geodesics. Finally we show this is also true for generalized Dirac operators.