Helicity Basis for Spin 1/2 and 1, and Discrete Symmetry Operations

TL;DR

This paper explores the properties of helicity basis states for spin 1/2 and 1 particles within Lorentz group representations, focusing on their behavior under discrete symmetries like parity, charge conjugation, and CP.

Contribution

It provides a detailed analysis of helicity eigenstates' transformation properties, highlighting their non-parity eigenstate nature and symmetry behaviors in Lorentz representations.

Findings

Helicity eigenstates are not parity eigenstates.

Properties under charge conjugation and CP are characterized.

Supports the idea of helicity basis in relativistic quantum theory.

Abstract

We study the theory of the (1/2,0)+(0,1/2) and (1,0)+(0,1) representations of the Lorentz group in the helicity basis. The helicity eigenstates are not the parity eigenstates. This is in accordance with the idea of Berestetskii, Lifshitz and Pitaevskii. The properties of the helicity eigenstates with respect to the charge conjugation and the CP- conjugation are also considered.