Fermions

In this section we present a first simple classical statistical model that is equivalent to a quantum field theory. It is a generalized Ising model which describes free massless fermions in one time and one space dimension. Even though this two-dimensional model remains extremely simple, all aspects of the formalism of quantum mechanics are already visible. This concerns both the Schr¨odinger or von Neumann equation for a unitary evolution and the appearance of non-commuting operators for observables like position or momentum.