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.

On the generalized spinor classification: beyond the Lounesto’s classification

“…where the operator E ( p) is responsible to change the spinor helicity of the Elko spinors [7]. In general, the ( p) operators, presented in (1) and 2, must satisfy certain conditions given in [7,22]. Furthermore, ( p) has to be idempotent, 2 ( p) = 1, ensuring an invertible mapping [22].…”

“…Let us assume ψ to be a given spinor belonging to a section of the vector bundle P Spin e 1,3 (M) × ρ C 4 , where ρ stands for the entire representation space D (1/2,0) ⊕ D (0,1/2) , or a given sector of such [10,11]. The bilinear quantities associated to ψ read 1 The presence of the abstract O operator stands for the new operators A and B, built in Ref. [3].…”

“…In fact, e J 0 is the charge density, whereas ec J k (i, j, k = 1, 2, 3) are identified to the (electric) current density [26]. Theh 2 K μ is interpreted as chiral current (spin density), conserved when m = 0 [1]. And, the quantity eh 2mc S i j is the magnetic moment density, while eh 2mc S 0 j is the electric moment density [18,[27][28][29].…”

“…The well known Lounesto's spinor classification is a comprehensive and exhaustive categorization based on the bilinear covariants that discloses the possibility of a large variety of spinors, comprising regular and singular spinors which includes the cases of Dirac, Weyl, and Majorana as very particular spinors [1].…”

New spinor classes on the Graf-Clifford algebra

“…In fact, the new mass dimension one spinors found in Ref. [36] may be employed to construct pure spinor superstring ghosts in a curved heterotic background [37].…”