Discrete Series for the Universal Covering Group of the 3 + 2 de Sitter Group
| Autor: | N. T. Evans |
|---|---|
| Rok vydání: | 1967 |
| Předmět: |
Algebra
Spin representation Pure mathematics Representation of a Lie group Induced representation Representation theory of the Lorentz group Representation theory of SU Fundamental representation Statistical and Nonlinear Physics (g K)-module Representation theory of the Poincaré group Mathematical Physics Mathematics |
| Zdroj: | Journal of Mathematical Physics. 8:170-184 |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/1.1705183 |
| Popis: | A classification is given of the irreducible unitary representations of the universal covering group of the 3 + 2 de Sitter group which contract to the usual physical representations of the Poincare group. These representations include the discrete series for the 3 + 2 de Sitter group. The classification problem is reduced from one for the group to the corresponding one for the Lie algebra. The method used by Thomas for the representations of the 4 + 1 de Sitter group is then followed, except that a representation is reduced out with respect to the irreducible unitary representations of a noncompact 2 + 2 subalgebra. It is conjectured that each representation of this subalgebra occurs at most once. The action on the representation spaces of a basis for the Lie algebra is given. The contractions of the representations to those of the Poincare, oscillator and the Galilei groups are briefly considered. |
| Databáze: | OpenAIRE |
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