Emergent spinor fields from exotic spin structures

TL;DR

This paper investigates how nontrivial spacetime topology leads to new classes of spinor fields through extended Clifford algebras, revealing a duality and fusion process between standard and exotic spinor classifications.

Contribution

It introduces an extended Clifford algebra framework to classify emergent spinor fields in multiply-connected spacetimes, uncovering a duality and fusion among spinor classes.

Findings

Discovered a duality between standard and exotic spinor classes.

Established a fusion process among spinor field classes.

Extended Clifford algebras naturally produce new algebraic spinor fields.

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.