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A product formula and combinatorial field theory | | A. Horzela
; P. Blasiak
; G.H.E. Duchamp
; K.A. Penson
; A.I. Solomon
; | | Date: |
22 Sep 2004 | | Subject: | Quantum Physics; Combinatorics | quant-ph math.CO | | Affiliation: | 1,4), G.H.E. Duchamp , K.A. Penson , A.I. Solomon (1,2) ( LPTL, University of Paris VI, France, The Open University, Milton Keynes, UK, LIPN, University of Paris-Nord, Villetaneuse, France, Institute of Nuclear Physics, Polish Academy of Sciences, K | | Abstract: | We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions - in essence, a combinatorial field theory. We apply these techniques to some examples related to specific physical Hamiltonians. | | Source: | arXiv, quant-ph/0409152 | | Services: | Forum | Review | PDF | Favorites | |
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