Boson normal ordering via substitutions and Sheffer-type polynomials

Blasiak, P.; Horzela, A.; Penson, K.A.; Duchamp, G.H.E. and Solomon, A.I. (2005). Boson normal ordering via substitutions and Sheffer-type polynomials. Physics Letters A, 338(2) pp. 108–116.

DOI: https://doi.org/10.1016/j.physleta.2005.02.028

URL: http://arxiv.org/abs/quant-ph/0501155

Abstract

We solve the boson normal ordering problem for
(q(a*)a + v(a*))^n with arbitrary functions q and v and integer n, where a and a* are boson annihilation and creation operators, satisfying [a,a*]=1. This leads to exponential operators generalizing the shift operator and we show that their action can be expressed in terms of substitutions. Our solution is naturally related through the coherent state representation to the exponential generating functions of Sheffer-type polynomials. This in turn opens a vast arena of combinatorial methodology which is applied to boson normal ordering and illustrated by a few examples.

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About

• Item ORO ID
• 6306
• Item Type
• Journal Item
• ISSN
• 0375-9601
• Extra Information
• Some of the symbols may not have transferred correctly into this bibliographic record and/or abstract.
• Keywords
• boson normal order; Sheffer-type polynomials; combinatorics
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Physical Sciences
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Allan Solomon