Canonical quantization of a massive Weyl field

TL;DR

This paper develops a consistent quantum theory for massive Weyl fields, highlighting the limitations of the Lagrange formalism and proposing Hamiltonian and extended Lagrangian approaches for canonical quantization.

Contribution

It introduces a novel Hamiltonian-based framework for quantizing massive Weyl fields and offers a new interpretation of the Majorana condition.

Findings

Standard Lagrange formalism is inadequate for massive Weyl spinors.

Hamilton and extended Lagrange formalisms enable consistent quantization.

New interpretation of the Majorana condition is proposed.

Abstract

We construct a consistent theory of a quantum massive Weyl field. We start with the formulation of the classical field theory approach for the description of massive Weyl fields. It is demonstrated that the standard Lagrange formalism cannot be applied for the studies of massive first-quantized Weyl spinors. Nevertheless we show that the classical field theory description of massive Weyl fields can be implemented in frames of the Hamilton formalism or using the extended Lagrange formalism. Then we carry out a canonical quantization of the system. The independent ways for the quantization of a massive Weyl field are discussed. We also compare our results with the previous approaches for the treatment of massive Weyl spinors. Finally the new interpretation of the Majorana condition is proposed.