Representations of the full Lorentz group in quantum field theory

Abstract

Various representations of the full Lorentz group are possible since the charge conjugation may be included into the realization of the parts of the group disjoint from the proper Lorentz transformations. Due to the antilinearity of charge conjugation in quantum mechanics (QM) and linearity in quantum field theory (QFT), these realizations differ in QM and QFT. Based on the observation that sign problems can be solved in relativistic quantum mechanics, it is shown that the second quantization of antiparticles can be modified to achieve consistency of QFT with QM. Modifications of the Wightman axioms are presented from which the existence of a unitary CPT transformation is derived.