Pin Groups in General Relativity

Abstract

There are eight possible Pin groups that can be used to describe the transformation behaviour of fermions under parity and time reversal. We show that only two of these are compatible with general relativity, in the sense that the configuration space of fermions coupled to gravity transforms appropriately under the space-time diffeomorphism group.

9 pages, added section 7 on the role of diffeomorphism invariance

References in corpus (1)

• Dirac operator on spinors and diffeomorphisms

Cited by in corpus (2)

• The Complete Barrett-Crane Model and its Causal Structure
• Spinor Representation of $O(3)$ for $S_4$