Network Models: Action formulation

TL;DR

This paper introduces a method to formulate quantum field theory on arbitrary networks using R-matrices and fermionic fields, enabling calculation of transition amplitudes and extension to multiparticle interactions.

Contribution

It presents a novel action formulation for network-based quantum field theory that generalizes existing methods and incorporates multiparticle interactions.

Findings

Method reproduces known results on bubble and triangle diagrams.

Allows calculation of transition amplitudes via Green functions.

Extends network models to include multiparticle interactions.

Abstract

We develop a technique to formulate quantum field theory on arbitrary network, based on different, randomly disposed sets of scattering's. We define R-matrix of the whole network as a product of R-matrices attached to each of scattering nods. Then an action for a network in terms of fermionic fields is formulated, which allows to calculate the transition amplitudes as their Green functions. On so-called bubble and triangle diagrams it is shown that the method produces the same results as the one which uses the generalized star product. The approach allows to extend network models by including multiparticle interactions at the scattering nods.