On the Spinor Representation

Abstract

A systematic study of the spinor representation by means of the fermionic physical space is accomplished and implemented. The spinor representation space is shown to be constrained by the Fierz-Pauli-Kofink identities among the spinor bilinear covariants. A robust geometric and topological structure can be manifested from the spinor space, wherein, for instance, the first and second homotopy groups play prominent roles on the underlying physical properties, associated to the fermionic fields.

16 pages

References in corpus (11)

• From Dirac spinor fields to ELKO
• Classification of Singular Spinor Fields and Other Mass Dimension One Fermions
• Exotic Dark Spinor Fields
• Bilinear Covariants and Spinor Fields Duality in Quantum Clifford Algebras
• On the bilinear covariants associated to mass dimension one spinors
• Spinor Fields Classification in Arbitrary Dimensions and New Classes of Spinor Fields on 7-Manifolds
• Questing for Algebraic Mass Dimension One Spinor Fields
• A generally-relativistic gauge classification of the Dirac fields
• The connection between Dirac dynamic and parity symmetry
• Quantum tomography for Dirac spinors
• The Spacetime of a Dirac Fermion

Cited by in corpus (6)

• Effective lagrangian for a mass dimension one fermionic field in curved spacetime
• On the generalized spinor classification: Beyond the Lounesto's Classification
• The (restricted) Inomata-McKinley spinor representation and the underlying topology
• A note on hidden classes in spinor classification
• Additional fermionic fields onto parallelizable 7-spheres
• Remarks on mass dimension one fermions: The underlying aspects, bilinear forms, Spinor Classification and RIM decomposition