Canonical quantization, path integral representations, and pseudoclassical description of massive Weyl neutrinos in external backgrounds

TL;DR

This paper develops a comprehensive quantum and classical framework for massive Weyl and Dirac neutrinos in external backgrounds, including path integral and pseudoclassical descriptions, with applications to neutrino physics.

Contribution

It introduces a novel Hamiltonian formulation and path integral representation for massive Weyl fields, extending the classical and quantum descriptions of neutrinos in external backgrounds.

Findings

Derived propagators for Weyl and Dirac neutrinos in external fields

Constructed pseudoclassical particle actions for neutrinos

Established connections between Weyl and Dirac propagators

Abstract

We study massive 1/2-spin particles in various external backgrounds keeping in mind applications to neutrino physics. We are mainly interested in massive Majorana (Weyl) fields. However, massive neutral Dirac particles are also considered. We formulate classical Lagrangian theory of the massive Weyl field in terms of Grassmann-odd two-component spinors. Then we construct the Hamiltonian formulation of such a theory, which turns out to be a theory with second-class constraints. Using this formulation we canonically quantize the massive free Weyl field. We derive propagators of the Weyl field and relate them to the propagator of a massive Dirac particle. We also study the massive Weyl particles propagating in the background mater. We find the path integral representation for the propagator of such a field, as well as the corresponding pseudoclassical particle action. The massless limit of the Weyl field interacting with the matter is considered and compared with results of other works. Finally, the path integral representation for the propagator of the neutral massive Dirac particle with an anomalous magnetic moment moving in the background matter and external electromagnetic field, as well as the corresponding pseudoclassical particle action are constructed.