Self/anti-self charge conjugate states in the helicity basis

TL;DR

This paper constructs and analyzes self/anti-self charge conjugate states for spin-1/2 particles in the helicity basis, exploring their properties, equations, and symmetries within quantum field theory, including implications for Majorana particles.

Contribution

It introduces a framework for Majorana-like states in the helicity basis, examining their symmetry properties, equations, and phase choices, extending previous formulations to higher spins.

Findings

Constructed self/anti-self charge conjugate states in the helicity basis.

Analyzed discrete symmetries and phase selection in these states.

Presented Dirac-like equations with doubled Fock space for these states.

Abstract

We construct self/anti-self charge conjugate (Majorana-like) states for the (1/2,0)+(0,1/2) representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problem of the basis rotations and that of the selection of phases in the Dirac-like and Majorana-like field operators are considered. The discrete symmetries properties (P, C, T) are studied. Particular attention has been paid to the question of (anti)commutation of the Charge conjugation operator and the Parity in the helicity basis. Dynamical equations have also been presented. In the (1/2,0)+(0,1/2) representation they obey the Dirac-like equation with eight components, which has been first introduced by Markov. Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino). The chirality and the helicity for Dirac and Majorana states have been discussed. PACS: 11.30.Cp, 11.30.Er, 11.30.Ly Keywords: Lorentz Group, Neutral Particles, Helicity Basis