Opening the Pandora's box of quantum spinor fields

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.

18 pages

References in corpus (9)

• Dynamical dispersion relation for ELKO dark spinor fields
• Exotic Dark Spinor Fields
• Hawking Radiation from Elko Particles Tunnelling across Black Strings Horizon
• Revealing how different spinors can be: the Lounesto spinor classification
• Spinor Fields Classification in Arbitrary Dimensions and New Classes of Spinor Fields on 7-Manifolds
• Questing for Algebraic Mass Dimension One Spinor Fields
• Dirac fields in f(R)-gravity with torsion
• Flag-dipole and flagpole spinors fluid flows in Kerr spacetimes
• Quantum tomography for Dirac spinors

Cited by in corpus (10)

• Constraints on mapping the Lounesto's Classes
• On the generalized spinor classification: Beyond the Lounesto's Classification
• Singular spinors and their connection
• New spinor classes on the Graf-Clifford algebra
• From Dipole spinors to a new class of mass dimension one fermions
• Subliminal aspects concerning the Lounesto's classification
• Spinorial structures, discrete symmetries and some consequences
• Emergent spinor fields from exotic spin structures
• Additional fermionic fields onto parallelizable 7-spheres
• New constrained generalized Killing spinor field classes in warped flux compactifications