World Spinors - Construction and Some Applications

TL;DR

This paper explores the topological double-coverings of certain groups, constructs their unitary irreducible representations, and introduces infinite-component spinorial fields called 'manifields' with applications to particle physics.

Contribution

It provides an explicit construction and classification of unitary irreducible representations of double-covered groups and introduces infinite-component 'manifields' for the first time.

Findings

Classified all $ar{SL}(n,R)$, $n=3,4$ unitary irreducible representations.

Constructed infinite-component spinorial and tensorial 'manifields'.

Determined particle content via the $ar{SL}(3,R)$ 'little' group.

Abstract

The existence of a topological double-covering for the $GL(n,R)$ and diffeomorphism groups is reviewed. These groups do not have finite-dimensional faithful representations. An explicit construction and the classification of all $\bar{SL}(n,R)$, $n=3,4$ unitary irreducible representations is presented. Infinite-component spinorial and tensorial $\bar{SL}(4,R)$ fields, "manifields", are introduced. Particle content of the ladder manifields, as given by the $\bar{SL}(3,R)$ "little" group is determined. The manifields are lifted to the corresponding world spinorial and tensorial manifields by making use of generalized infinite-component frame fields. World manifields transform w.r.t. corresponding $\bar{Diff}(4,R)$ representations, that are constructed explicitly.