EXOTIC MAJORANA SPINORS IN (3+1)-DIMENSIONAL SPACE-TIMES

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.