Exotic Majorana spinors in (3+1)-dimensional space–times

Abstract

Inequivalent spin structures on Lorentzian manifolds are studied and in particular the possibility of defining inequivalent Majorana spinors associated with real irreducible representations of the Clifford algebra corresponding to a metric of signature (3,1) is analyzed. Such exotic complex (Dirac) spinors were first discussed in 1979. It is shown that exotic real (Majorana) spinors can be defined in a consistent way, too. The main idea is the use of a ‘‘chiral’’ U(1) group instead of a ‘‘complex’’ U(1) which contains all the relevant topological information. This result may be interesting in the context of the geometry of supergravity–matter coupling.