PCT, spin and statistics, and analytic wave front set

A new, more general derivation of the spin-statistics and PCT theorems is presented. It uses the notion of the analytic wave front set of (ultra)distributions and, in contrast to the usual approach, covers nonlocal quantum fields. The fields are defined on the functional domain of test functions with compact supports in the momentum space. The vacuum expectation values are thereby admitted to be arbitrarily singular in their space–time dependence. The local commutativity condition is replaced by an asymptotic commutativity condition, which develops generalizations of the microcausality axiom previously proposed.