Eur. Phys. J. C (2018) 78: 157
https://doi.org/10.1140/epjc/s10052-018-5631-5

Regular Article - Theoretical Physics

Opening the Pandora’s box of quantum spinor fields

¹ International School for Advanced Studies-SISSA, Via Bonomea 265, 34136, Trieste, Italy
² Departamento de Física e Química, Universidade Estadual Paulista-UNESP, Guaratinguetá, SP, Brazil
³ Centro de Matemática, Computação e Cognição, Universidade Federal do ABC-UFABC, 09210-580, Santo André, Brazil

^* e-mail: roldao.rocha@ufabc.edu.br

Received: 2 November 2017
Accepted: 11 February 2018
Published online: 23 February 2018

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.