Path Integrals for Stochastic Neurodynamics Path Integrals for Stochastic Neurodynamics

We present here a method for the study of stochastic neurodynamics in the framework of the "Neural Network Master Equation" proposed by Cowan. We consider a model neural network composed of two{state neurons subject to simple stochastic kinetics. We introduce a method based on a spin choerent state path integral to compute the moment generating function of such a network. A formal construction of the path integral is presented and the general expression for many neuron networks is obtained. We show explicitly that the method enables us to obtain the exact moment generating function for a single neuron case. Possible directions for the analysis of many neuron networks as well as an alternative path integral formulation are discussed.