A product formula and combinatorial field theory

Horzela, A.; Blasiak, P.; Duchamp, G. E. H.; Penson, K. A. and Solomon, A. I. (2004). A product formula and combinatorial field theory. In: Proceedings of the XI International Conference on Symmetry Methods in Physics (SYMPHYS-11), 21-24 Jun 2004, Prague.

URL: http://www1.jinr.ru/Proceedings/Burdik-2004/index....

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.

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