Generalization of thePCTtheorem to all discrete space-time symmetries in quantum field theories

Abstract

The methodology of the $\mathrm{PCT}$ theorem is applied to all discrete space-time symmetries in the framework of the Wightman formalism. New conditions which hold at Jost points only are introduced and their significance is pointed out. A general theorem is proven according to which in a field theory satisfying the Wightman axioms, with the possible exception of local commutativity, if any discrete space-time symmetry holds at all points then there is a corresponding condition which holds at Jost points and vice versa. Possible links among various symmetries are investigated and two corollaries of the above theorem are formulated. Finally, some applications to both symmetry-preserving and symmetry-violating theories are discussed.