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hal-00004077, version 1

Boson Normal Ordering via Substitutions and Sheffer-type Polynomials

P Blasiak, A Horzela, K A Penson 1, G H E Duchamp 2, A I Solomon

(2005)

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.

  • 1:  Laboratoire de Physique Théorique des Liquides (LPTL)
  • CNRS : UMR7600 – Université Pierre et Marie Curie [UPMC] - Paris VI
  • 2:  Laboratoire d'informatique de Paris-nord (LIPN)
  • CNRS : UMR7030 – Université Paris XIII - Paris Nord
  • Domain : Physics/Quantum Physics
    Mathematics/Combinatorics
    Computer Science/Discrete Mathematics
  • Keywords : boson normal ordering problem – coherent states – Sheffer-type polynomials – generating functions
  • Comment : 10 pages – 24 references
 
  • hal-00004077, version 1
  • http://hal.archives-ouvertes.fr/hal-00004077
  • oai:hal.archives-ouvertes.fr:hal-00004077
  • From: Gérard Henry Edmond Duchamp <>
  • Submitted on: Thursday, 27 January 2005 03:21:10
  • Updated on: Thursday, 27 January 2005 03:21:10