Quantization of massive Weyl fields in vacuum

TL;DR

This paper reviews methods for quantizing massive Weyl fields in vacuum, addressing classical descriptions with Grassmann variables and commuting spinors, and introduces a new quantization approach for commuting fields.

Contribution

It provides a comparative analysis of classical and quantum descriptions of Weyl fields and proposes a novel quantization method for commuting classical fields.

Findings

Correct anticommutation relations achieved

Proper total energy form obtained

New quantization method for commuting fields introduced

Abstract

We briefly review the main methods for the description of massive Weyl fields in vacuum. On the classical level we discuss Weyl fields expressed through Grassmann variables as well as having spinors with commuting components. In both approaches we quantize the system. We get the correct anticommutation relations between creation and annihilation operators, which result in the proper form of the total energy of the field. However, the commuting classical Weyl fields require the new method of quantization.