Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-04-17
Found.Phys. 27 (1997) 1105-1122
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages, TeX
Scientific paper
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.
Ne'eman Yuval
Sijacki Djordje
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