Galilei-invariant quantum field theories with pair interaction review

We exhibit a class of quantum field theories where particles interact with pair potentials and for which the time evolution exists in the Heisenberg representation. The essential condition for existence is the stability in the thermodynamic sense and this is achieved by having the interaction fall off with the relative momenta of the particles. This can be done in a Galilei-invariant manner. We show that these systems have some mixing behaviour which one postulates in ergodic theory but difficult to prove for classical systems. (Authors) 59 refs