Field theory for biophysical neural networks

The human brain is a complex system composed of a network of hundreds of billions of discrete neurons that are coupled through time dependent synapses. Simulating the entire brain is a daunting challenge. Here, we show how ideas from quantum field theory can be used to construct an effective reduced theory, which may be analyzed with lattice computations. We give some examples of how the formalism can be applied to biophysically plausible neural network models.