Equations of motion in odd-dimensional spaces and T-, C-invariance

Abstract

The properties of the equation of Dirac type in three-dimensional and five-dimensional Minkowski space-time with respect to time reflection (in sense of Pauli and Wigner) as well as to the operation of charge conjugation are investigated. P-, T-, C-invariance of Dirac equation for the cases of four components (in three-dimentional space) and eight components (in five-dimensional space) is established. Within the framework of the Poincare group a relativistic equation is suggested wich describes the movement of a particle with non-fixed (indefinite) mass in external electromagnetic field.