T and C Symmetry Breaking in Algebraic Quantum Field Theory ^†

Abstract

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra). The proposed approach is based on the use of Grassmann densities in the momentum space and their derivatives with respect to the construction from these densities of both basis Clifford vectors of spacetime and the spinor vacuum. We have shown the existence of two vacua: normal and alternative. We have proven that CPT is the real structure operator in the theory of Krein spaces. C and T operators transform a normal vacuum into an alternative one, which leads to the breaking of these symmetries.