On the algebra of symmetries of Laplace and Dirac operators
| Autor: | Joris Van der Jeugt, Roy Oste, Hendrik De Bie |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Angular momentum
Dirac operator Dirac (software) FOS: Physical sciences 01 natural sciences symbols.namesake Operator (computer programming) Bannai-Ito algebra 81Q80 81R10 81R99 47L90 0103 physical sciences FOS: Mathematics Representation Theory (math.RT) 0101 mathematics EQUATIONS Mathematical Physics Mathematics Dunkl operator 010308 nuclear & particles physics 010102 general mathematics Statistical and Nonlinear Physics Mathematical Physics (math-ph) Algebra Mathematics and Statistics Laplace operator Symmetry algebra symbols Angular momentum operator Symmetry (geometry) DUNKL OPERATORS Mathematics - Representation Theory |
| Zdroj: | LETTERS IN MATHEMATICAL PHYSICS |
| ISSN: | 0377-9017 1573-0530 |
| Popis: | We consider a generalization of the classical Laplace operator, which includes the Laplace-Dunkl operator defined in terms of the differential-difference operators associated with finite reflection groups called Dunkl operators. For this Laplace-like operator, we determine a set of symmetries commuting with it, which are generalized angular momentum operators, and we present the algebraic relations for the symmetry algebra. In this context, the generalized Dirac operator is then defined as a square root of our Laplace-like operator. We explicitly determine a family of graded operators which commute or anti-commute with our Dirac-like operator depending on their degree. The algebra generated by these symmetry operators is shown to be a generalization of the standard angular momentum algebra and the recently defined higher rank Bannai-Ito algebra. 39 pages, final version |
| Databáze: | OpenAIRE |
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