Bilinear Covariants and Spinor Fields Duality in Quantum Clifford Algebras

Abstract

Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields is thus discussed. Hence, by endowing the underlying spacetime with an arbitrary bilinear form with a antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are therefore compared to the classical (non quantum) ones. Classes of quantum spinor fields are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles, dipoles and flag-dipoles ones as well. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.

21 pages, J. Math. Phys. (in press)

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Cited by in corpus (12)

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• Elko and mass dimension one field of spin one half: causality and Fermi statistics
• Weyl and Majorana Spinors as Pure Goldstone Bosons
• Fermionic dark matter-photon quantum interaction: A mechanism for darkness
• The Heisenberg spinor field classification and its interplay with the Lounesto's classification
• Singular spinors as expansion coefficients of local spin-half fermionic and bosonic fields: On the two-fold Wigner degeneracy
• On the bundle of Clifford algebras over the space of quadratic forms
• Geometry of spinors: doubly-chiral plane-wave expansion
• Necessity of Tensorial Connections for Spinorial Systems
• Emergent spinor fields from exotic spin structures
• General Spin Sums in Quantum Field Theory
• Angular-Radial Integrability of Coulomb-like Potentials in Dirac Equations