Helicity Basis and Parity

TL;DR

This paper explores the helicity basis for spinor representations, highlighting its non-invariance under parity, and introduces a new parity operator that commutes with the Hamiltonian, linking to quantum field theory.

Contribution

It introduces a novel form of the parity operator in the helicity basis that commutes with the Hamiltonian, expanding the understanding of parity in quantum field theory.

Findings

Helicity eigenstates are not parity eigenstates.

A new parity operator commuting with the Hamiltonian is proposed.

Relations to Gelfand-Tsetlin-Sokolik quantum field theory are discussed.

Abstract

We study the theory of the (1/2,0)+(0,1/2) representation in helicity basis. Helicity eigenstates are not the parity eigenstates. This is in accordance with the consideration of Berestetskii, Lifshitz and Pitaevskii. Relations to the Gelfand-Tsetlin-Sokolik-type quantum field theory are discussed. Finally, a new form of the parity operator is proposed. It commutes with the Hamiltonian.