Statistical Neural Field Theory

In 1972, 1973 Wilson and Cowan introduced a mathematical model for the population dynamics of nets of interacting neurons, based on a mean field description of the activity. In 1978 Cowan (unpublished) showed that such a mean field can be derived from a master equation, and in 1991 that such a master equation can be conveniently represented in terms of the annihilation and creation operators of a quantum field theory.  In effect, neural nets can be represented in terms of quantum spins.  The resulting theory (Ohira & Cowan 1993) proved difficult to calculate.  Recently Buice & Cowan (in preparation) have found a more tractable way to represent such quantum spins, and to calculate (perturbatively) the effects of fluctuations and correlations in such nets beyond the range of mean field theory.  A short account of this will be given.