P, C and T: Different Properties on the Kinematical Level

TL;DR

This paper investigates how discrete symmetries P, C, and T are defined and behave at the kinematical level within the extended Poincare Group across various bases and representations, revealing ambiguities with physical implications.

Contribution

It provides a detailed analysis of the definitions and properties of P, C, and T operators in different bases and representations, highlighting ambiguities and their physical consequences.

Findings

Ambiguities in defining P, C, T operators depend on the basis and representation.

Differences in operator properties lead to distinct physical outcomes.

Helicity basis properties influence the symmetry operator definitions.

Abstract

We study the discrete symmetries (P,C and T) on the kinematical level within the extended Poincare Group. On the basis of the Silagadze research, we investigate the question of the definitions of the discrete symmetry operators both on the classical level, and in the secondary-quantization scheme. We study the physical contents within several bases: light-front formulation, helicity basis, angular momentum basis, and so on, on several practical examples. We analise problems in construction of the neutral particles in the the (1/2,0)+(0,1/2) representation, the (1,0)+(0,1) and the (1/2,1/2) representations of the Lorentz Group. As well known, the photon has the quantum numbers 1^-, so the (1,0)+(0,1) representation of the Lorentz group is relevant to its description. We have ambiguities in the definitions of the corresponding operators P, C; T, which lead to different physical consequences. It appears that the answers are connected with the helicity basis properties, and commutations/anticommutations of the corresponding operators, P, C, T, and C^2, P^2, (CP)^2 properties.