Axial momentum and quantization of the Majorana field

TL;DR

This paper introduces a novel quantization method for the Majorana field based on axial momentum eigenfunctions, revealing its underlying Clifford algebra structure and constructing Poincaré, parity, and time reversal operators.

Contribution

It presents a new approach to Majorana field quantization using axial momentum eigenfunctions guided by relativistic invariance, avoiding canonical formalism.

Findings

Revealed the real Clifford algebra structure of the quantized Majorana field.

Constructed Poincaré transformation generators without classical correspondence.

Developed operators for parity and time reversal symmetry.

Abstract

New approach to quantization of the relativistic Majorana field is presented. It is based on expansion of the field into eigenfunctions of the axial momentum -- a novel observable introduced recently. Relativistic invariance is used as the main guiding principle instead of canonical formalism. Hidden structure of the quantized Majorana field in the form of real Clifford algebra of Hermitian fermionic operators is unveiled. Generators of the Poincar\'e transformations in the Fock space are found as solutions of certain operator equations, without invoking the principle of correspondence with classical conserved quantities. Also operators of parity $\hat{\mbox{P}}$ and time reversal $\hat{\mbox{T}}$ are constructed.