World Spinors - Construction and Some Applications

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 $\overline{SL}(n,R)$, $n=3,4$ unitary irreducible representations is presented. Infinite-component spinorial and tensorial $\overline{SL}(4,R)$ fields, "manifields", are introduced. Particle content of the ladder manifields, as given by the $\overline{SL}(3,R)$ "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 $\overline{Diff}(4,R)$ representations, that are constructed explicitly.

19 pages, TeX

References in corpus (1)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance

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