Space--Time Symmetry, CPT and Mirror Fermions

The motivations for the construction of an 8-component representation of fermion fields based on a two dimensional representation of time reversal transformation and CPT invariance are discussed. Some of the elementary properties of the quantum field theory in the 8-component representation are studied. It includes the space-time and charge conjugation symmetries, the implementation of a reality condition, the construction of interaction theories, the field theoretical imaginary- and real-time approach to thermodynamics of fermionic systems, the quantization of fermion fields, their particle content and the Feynman rules for perturbation theories. It is shown that in the new presentation, a CPT violation can be formulated in principle. The construction of interaction theories in the 8-component theory for fermions is shown to be constrained by the CPT invariance. The short distance behavior and relativistic covariance are studied. In the path integral representation of the thermodynamical potential, the conventional imaginary-time approach is shown to be smoothly connected to a real-time thermal field theory in the 8-component representation for fermion fields without any additional subtraction of infinities. The metastability at zero density and the nature of the spontaneous CP violation in color superconducting phases of strong interaction ground states are clarified.