World Spinors: Group Representations and Field Equations

TL;DR

This paper explores the algebraic structure, constraints, and physical interpretation of world spinors, analyzing their transformation properties under affine and diffeomorphism groups, and presents a geometric framework and specific equations in 3D.

Contribution

It introduces a geometric construction for world spinors using an infinite-component generalization of frame fields and examines their wave equations in curved spacetime.

Findings

Relations between spinorial wave equations and symmetry groups are established

A geometric framework for world spinors is proposed

The world spinor equation in 3D is detailed

Abstract

The questions of the existence, basic algebraic properties and relevant constraints that yield a viable physical interpretation of world spinors are discussed in details. Relations between spinorial wave equations that transform respectively w.r.t. the tangent flat-space (anholonomic) Affine symmetry group and the world generic-curved-space (holonomic) group of Diffeomorphisms are presented. A geometric construction based on an infinite-component generalization of the frame fields (e.g. tetrads) is outlined. The world spinor field equation in 3D is treated in more details.