A product formula and combinatorial field theory


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.


    3 Figures and Tables

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