Network models: Action formulation

We develop a technique to formulate quantum field theory on an arbitrary network, based on different randomly disposed sets of scattering points. We define the R-matrix of the whole network as a product of R-matrices attached to each scattering node. Then an action is formulated for a network in terms of fermionic fields, which allows to calculate the transition amplitudes as 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 nodes.