Spinorial matter and general relativity theory

Dj. Sijacki

Abstract: World spinors, the spinorial matter (particles, $p$-branes and fields) in a generic curved space is considered. Representation theory, as well as the basic algebraic and topological properties of relevant symmetry groups are presented. 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. World spinor equations and certain basic constraints that yield a viable physical theory are discussed. 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.

Keywords: General relativity, world spinors, Dirac-like equation, $SL(n,{\Bbb R})$ representations

Classification (MSC2000): 22E46, 22E65, 58B25, 81T20, 83D05

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