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arXiv · 1703.02153

A novel approach to perturbative calculations for a large class of interacting boson theories

Kamil Bradler
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Abstract

We present a method of calculating the interacting S-matrix to an arbitrary perturbative order for a large class of boson interaction Lagrangians. The method takes advantage of a previously unexplored link between the $n$-point Green's function and a certain system of linear Diophantine equations. By finding all nonnegative solutions of the system, the task of perturbatively expanding an interacting $S$-matrix becomes elementary for any number of interacting fields, to an arbitrary perturbative order (irrespective of whether it makes physical sense) and for a large class of scalar boson theories. The method does not rely on the position-based Feynman diagrams and promises to be extended to many perturbative models typically studied in quantum field theory. Aside from interaction field calculations we showcase our approach by expanding a pair of Unruh-DeWitt detectors coupled to Minkowski vacuum to an arbitrary perturbative order in the coupling constant. We also link our result to Hafnian as introduced by Caianiello and present a method to list all (2n-1)!! perfect matchings of a complete graph on 2n vertices.

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Kamil Bradler. 2018-02-07. A novel approach to perturbative calculations for a large class of interacting boson theories. https://doi.org/10.1016/j.nuclphysb.2017.11.007

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