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

Research paper by Gunnar Sigurdsson, Sergei D. Silvestrov

Indexed on: 12 Nov '03Published on: 12 Nov '03Published in: Mathematics - Quantum Algebra

#### 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.