A geometrical interpretation of the Pauli exclusion principle in classical field theory

It is shown that classical Dirac fields with the same couplings obey the Pauli exclusion principle in the following sense: If at a certain time two Dirac fields are in different states, they can never reach the same one. This is geometrically interpreted as analogous to the impossibility of crossing of trajectories in the phase space of a dynamical system. An application is made to a model in which extended particles are represented as solitary waves of a set of several fundamental, confined nonlinear Dirac fields, with the result that the same mechanism accounts both for fermion and boson behaviors.