Bibliographic Citation
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| DOI | 10.1063/1.1915291 |
| Title | On the Casimir of the group ISL(n,R) and its algebraic decomposition |
| Creator/Author | Pecina-Cruz, J.N. [Bureau of Economic Geology, J.J. Pickle Research Campus, University of Texas at Austin, University Station, Box X, Austin, Texas 78713-8294 (United States)] |
| Publication Date | 2005 Jun 01 |
| OSTI Identifier | OSTI ID: 20699203 |
| Other Number(s) | Journal ID: ISSN 0022-2488; JMAPAQ; TRN: US06A5354015205 |
| Resource Type | Journal Article |
| Resource Relation | Journal Name: Journal of Mathematical Physics; Journal Volume: 46; Journal Issue: 6; Other Information: DOI: 10.1063/1.1915291; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA) |
| Subject | 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CASIMIR OPERATORS; CLASSIFICATION; GAUGE INVARIANCE; GROUP THEORY; IRREDUCIBLE REPRESENTATIONS; QUANTUM GRAVITY; TENSORS |
| Description/Abstract | In this paper, an explicit expression for the Casimir operator (or the Casimir invariant) of the inhomogeneous group ISL(n,R) in its enveloping algebra is proposed, which using contractions of the tensorial indices of the generating operators P{sup {rho}} and E{sub {mu}}{sup {nu}} may be presented in the following [slightly more comprehensible as Eq. (1)] form. The Casimir is obtained by symmetrizing this expression. This tensor form is useful in the classification of particles in affine gravitational gauge theories; such as that based on ISL(4,R). It is also proven that the Casimir of ISL(n,R) can be decomposed in terms of the Casimirs of its little groups, a key point in the posterior construction of its irreducible representations. |
| Country of Publication | United States |
| Language | English |
| Format | Medium: X; Size: page(s) 063503-063503.5 |
| System Entry Date | 2010 Jun 03 |
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