A product formula and combinatorial field theory

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.

Presented at the XI International Conference on Symmetry Methods in Physics (SYMPHYS-11), Prague, Czech Republic, June 21-24, 2004. 17 pages, 36 references, 3 f