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A product formula and combinatorial field theory

A. Horzela·P. Blasiak·G. H. E. Duchamp·K. A. Penson·A. I. Solomon
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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.

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A. Horzela, P. Blasiak, G. H. E. Duchamp, K. A. Penson, A. I. Solomon. 2004-09-22. A product formula and combinatorial field theory. https://arxiv.org/abs/quant-ph/0409152

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