Little group generators for Dirac neutrino one-particle states

TL;DR

This paper derives the little group generators for Dirac neutrino states, revealing their roles as rotation operators that induce helicity flips, charge conjugation, and their combination, with implications for neutrino symmetry transformations.

Contribution

It provides explicit forms of the little group generators for Dirac neutrinos in terms of states and operators, and analyzes their physical transformation properties.

Findings

Generators induce helicity flip, charge conjugation, and combined transformations.

Transformations act as rotations in the Hilbert space of states.

Some transformations persist for chiral fields without mixing.

Abstract

Assuming neutrinos to be of the Dirac type, the little group generators for the one-particle states, created off the vacuum by the field operator, are obtained, both in terms of the one-particle states themselves and in terms of creation/annihilation operators. It is shown that these generators act also as rotation operators in the Hilbert space of the states, providing three types of transformations: a helicity flip, the standard charge conjugation, and a combination of the two, up to phases. The transformations' properties are provided in detail and their physical implications discussed. It is also shown that one of the transformations continues to hold for chiral fields without mixing them.