Pin Groups in General Relativity

TL;DR

This paper investigates the compatibility of different Pin groups with general relativity, identifying which of the eight possible groups correctly describe fermion transformations under spacetime symmetries.

Contribution

It demonstrates that only two of the eight Pin groups are compatible with general relativity's transformation requirements for fermions.

Findings

Only two Pin groups are compatible with general relativity.

The configuration space of fermions transforms correctly under these groups.

The study clarifies the mathematical structure of fermion transformations in curved spacetime.

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.