Bosonic realizations of the color analogue of the Heisenberg Lie algebra
Sigurdsson, Gunnar; Silvestrov, Sergei (2003). Bosonic realizations of the color analogue of the Heisenberg Lie algebra. Preprints in Mathematical Sciences, 2003, (4)
|
Unpublished
|
English
Authors:
Sigurdsson, Gunnar
;
Silvestrov, Sergei
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Project:
Non-commutative Analysis of Dynamics, Fractals and Wavelets
Non-commutative Geometry in Mathematics and Physics
Research Group:
Non-commutative Geometry-lup-obsolete
Abstract:
We describe realizations of the color analogue
of the Heisenberg Lie algebra by power series in non-commuting indeterminates satisfying Heisenberg's canonical commutation relations of quantum mechanics. The obtained formulas are used to construct new operator
representations of the color analogue of the Heisenberg Lie algebra. These representations are shown to be closely connected with some combinatorial identities and functional difference-differential interpolation formulae involving Euler, Bernoulli and Stirling numbers.
Keywords:
Heisenberg Lie algebra ;
combinatorial identities ;
representations ;
functional difference-differential interpolation ;
Bernoulli and Stirling numbers ;
Euler
Cite this