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The total angular momentum algebra related to the [formula omitted] Dunkl Dirac equation.
- Source :
-
Annals of Physics . Feb2018, Vol. 389, p192-218. 27p. - Publication Year :
- 2018
-
Abstract
- We consider the symmetry algebra generated by the total angular momentum operators, appearing as constants of motion of the S 3 Dunkl Dirac equation. The latter is a deformation of the Dirac equation by means of Dunkl operators, in our case associated to the root system A 2 , with corresponding Weyl group S 3 , the symmetric group on three elements. The explicit form of the symmetry algebra in this case is a one-parameter deformation of the classical total angular momentum algebra s o ( 3 ) , incorporating elements of S 3 . This was obtained using recent results on the symmetry algebra for a class of Dirac operators, containing in particular the Dirac–Dunkl operator for arbitrary root system. For this symmetry algebra, we classify all finite-dimensional, irreducible representations and determine the conditions for the representations to be unitarizable. The class of unitary irreducible representations admits a natural realization acting on a representation space of eigenfunctions of the Dirac Hamiltonian. Using a Cauchy–Kowalevski extension theorem we obtain explicit expressions for these eigenfunctions in terms of Jacobi polynomials. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00034916
- Volume :
- 389
- Database :
- Academic Search Index
- Journal :
- Annals of Physics
- Publication Type :
- Academic Journal
- Accession number :
- 127962882
- Full Text :
- https://doi.org/10.1016/j.aop.2017.12.015