Bosonic realizations of the color analogue of the Heisenberg Lie algebra

Gunnar Sigurdsson, Sergei Silvestrov

Research output: Contribution to journalArticle

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.
Original languageEnglish
Number of pages46
JournalPreprints in Mathematical Sciences
Volume2003
Issue number4
Publication statusUnpublished - 2003

Subject classification (UKÄ)

  • Mathematics

Keywords

  • Heisenberg Lie algebra
  • combinatorial identities
  • representations
  • functional difference-differential interpolation
  • Bernoulli and Stirling numbers
  • Euler

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