Bosonic realizations of the color analogue of the Heisenberg Lie algebra

Details Bosonic realizations of the color analogue of the Heisenberg Lie algebra Bosonic realizations of the color analogue of the Heisenberg Lie algebra

2003-11-12

arxiv.org/abs/math/0311204v1

Mathematics

Quantum Algebra

48 pages, LaTeX

Scientific paper

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.

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