  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.
