A gauge theory of CPT transformations to first order

The CPT symmetry is made local for the Dirac field and an analogous local symmetry is proposed for curved spacetime. A nontrivial, infinitesimal variation of the Dirac action is thus induced. It is shown that the metric spin connection of general relativity cannot accommodate this symmetry. A new gauge field is therefore introduced, which turns out to be a real pseudovector field, and its equations of motion are derived.