ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Two different approaches are used to construct infinite-component spinor equations based on the multiplicity-free irreducible representations of S¯L¯(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 S¯O¯(4) of S¯L¯(4,R) is "physical.'' A vector operator X μ is constructed directly in the infinite-dimensional reducible representation Ddisc( 1/2 ,0) ⊕Ddisc(0, 1/2 ). In the second approach, SL(2,C) and a vector operator γ μ are embedded directly in S¯L¯(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 j1, in the ( j1, j2) reduction over S¯O¯(4). Both manifields can fit the observed mass spectrum.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.526646
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