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Title: Variations of (pseudo-)rotations and the Laplace-Beltrami operator on homogeneous spaces

In this paper we obtain the Lie derivatives of the scalar parameters in the generalized Euler decomposition with respect to arbitrary axes under left and right deck transformations. This problem can be directly related to the representation of the angular momentum in quantum mechanics. As a particular example, we calculate the angular momentum and the corresponding quantum hamiltonian in the standard Euler and Bryan representations. Similarly, in the hyperbolic case, the Laplace-Beltrami operator is retrieved for the Iwasawa decomposition. The case of two axes is considered as well.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, 1 Hristo Smirnenski Blvd., 1046 Sofia (Bulgaria)
  2. Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia (Bulgaria)
  3. Institute of Biophysics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 21, 1113 Sofia (Bulgaria)
Publication Date:
OSTI Identifier:
22492616
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1684; Journal Issue: 1; Conference: AMiTaNS'15: 7. international conference for promoting the application of mathematics in technical and natural sciences, Albena (Bulgaria), 28 Jun - 3 Jul 2015; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; DECOMPOSITION; HAMILTONIANS; LAPLACIAN; LIE GROUPS; MATHEMATICAL SPACE; QUANTUM MECHANICS; ROTATION; SCALARS; VARIATIONS