Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-04-17
Acta Phys.Polon. B29 (1998) 1089
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
10 pages, LaTeX2e, Workshop on "Gauge Theories of Gravitation" Jadwisin, Poland, 4-10 Sept. 1997
Scientific paper
World spinors are objects that transform w.r.t. double covering group $\bar{Diff}(4,R)$ of the Group of General Coordinate Transformations. The basic mathematical results and the corresponding physical interpretation concerning these, infinite-dimensional, spinorial representations are reviewed. The role of groups $Diff(4,R)$, $GA(4,R)$, $GL(4,R)$, $SL(4,R)$, $SO(3,1)$ and the corresponding covering groups is pointed out. New results on the infinite dimensionality of spinorial representations, explicit construction of the $\bar{SL}(4,R)$ representations in the basis of finite-dimensional non-unitary $SL(2,C)$ representations, $SL(4,R)$ representation regrouping of tensorial and spinorial fields of an arbitrary spin lagrangian field theory, as well as its $SL(5,R)$ generalization in the case of infinite-component world spinor and tensor field theories are presented.
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