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Spinorial infinite equations fitting metric-affine gravity

Journal Article · · J. Math. Phys. (N.Y.); (United States)
DOI:https://doi.org/10.1063/1.526646· OSTI ID:6156337
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Two different approaches are used to construct infinite-component spinor equations based on the multiplicity-free irreducible representations of SL(4,R). These ''manifield'' equations are SL(2,C) invariant; they exist in special relativity, and can directly be coupled to gravitation in the metric-affine theory, i.e., in Einstein's general relativity with nonpropagating torsion and nonmetricity. In the first approach the maximal compact subgroup SO(4) of SL(4,R) is ''physical.'' A vector operator X/sup tsmu/ is constructed directly in the infinite-dimensional reducible representation D/sup disc/(1/2, 0) direct-sumD/sup disc/(0, 1/2). In the second approach, SL(2,C) and a vector operator ..gamma../sup tsmu/ are embedded directly in SL(4,R) via the Dirac representation. A manifield equation is then constructed (in a manner analogous to the Majorana equation) by taking an infinite-dimensional irreducible multiplicity-free representation of SL(4,R), spinorial in j/sub 1/, in the (j/sub 1/, j/sub 2/) reduction over SO(4). Both manifields can fit the observed mass spectrum.

Research Organization:
Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
DOE Contract Number:
AS05-76ER03992
OSTI ID:
6156337
Journal Information:
J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:12; ISSN JMAPA
Country of Publication:
United States
Language:
English

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Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMMUTATION RELATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
GRAVITATION
GROUP THEORY
INVARIANCE PRINCIPLES
IRREDUCIBLE REPRESENTATIONS
LAGRANGIAN FUNCTION
LIE GROUPS
LORENTZ INVARIANCE
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
POINCARE GROUPS
QUANTUM FIELD THEORY
RELATIVITY THEORY
SL GROUPS
SO GROUPS
SPINOR FIELDS
SPINORS
SYMMETRY GROUPS
TENSORS
UNITARITY
VECTORS
WAVE EQUATIONS