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A product formula and combinatorial field theory

By A. Horzela, P. Blasiak, G. E. H. Duchamp, K. A. Penson and A. I. Solomon

Abstract

We treat the problem of normally ordering expressions involving the standard boson operators a, ay where [a; ay] = 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 eld theory. We apply these techniques to some examples related to specic physical Hamiltonians

Year: 2004
OAI identifier: oai:oro.open.ac.uk:20813
Provided by: Open Research Online

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