Opening the Pandora's box of quantum spinor fields

TL;DR

This paper explores extending Lounesto's classical spinor classification into the quantum field theory framework, analyzing bilinear covariants and proposing a quantum reconstruction algorithm for various spinor types.

Contribution

It introduces a novel approach to classify spinors in second quantization, expanding the classical framework and extending the Feynman propagator to all spinor classes.

Findings

Extended bilinear covariants in quantum spinor fields

Proposed quantum reconstruction algorithm for spinors

Extended Feynman propagator for all spinor classes

Abstract

Lounesto's classification of spinors is a comprehensive and exhaustive algorithm that, based on the bilinears covariants, discloses the possibility of a large variety of spinors, comprising regular and singular spinors and their unexpected applications in physics and including the cases of Dirac, Weyl, and Majorana as very particular spinor fields. In this paper we pose the problem of an analogous classification in the framework of second quantization. We first discuss in general the nature of the problem. Then we start the analysis of two basic bilinear covariants, the scalar and pseudoscalar, in the second quantized setup, with expressions applicable to the quantum field theory extended to all types of spinors. One can see that an ampler set of possibilities opens up with respect to the classical case. A quantum reconstruction algorithm is also proposed. The Feynman propagator is extended for spinors in all classes.