Emergent spinor fields from exotic spin structures
arXiv:2302.08473 · doi:10.1093/ptep/ptae049
Abstract
The classification of emergent spinor fields according to modified bilinear covariants is scrutinized, in spacetimes with nontrivial topology, which induce inequivalent spin structures. Extended Clifford algebras, constructed by equipping the underlying spacetime with an extended bilinear form with additional terms coming from the nontrivial topology, naturally yield emergent extended algebraic spinor fields and their subsequent extended bilinear covariants, which are contrasted to the classical spinor classification. An unexpected duality between the standard and the exotic spinor field classes is therefore established, showing that a complementary fusion process among the spinor field classes sets in, when extended Clifford bundles are addressed in multiply-connected spacetimes.
16 pages, 2 figures; final version published in PTEP
References in corpus (9)
- Classification of Singular Spinor Fields and Other Mass Dimension One Fermions
- Exotic Dark Spinor Fields
- Quantum simulation of non-trivial topology
- Bilinear Covariants and Spinor Fields Duality in Quantum Clifford Algebras
- The quadratic spinor Lagrangian, axial torsion current, and generalizations
- 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
- Quantum tomography for Dirac spinors
- The (restricted) Inomata-McKinley spinor representation and the underlying topology