Equal-time commutators, fixed point theorems, superconvergency and PCAC in the Lee model

Abstract

It is shown that some properties characteristic of the real physical theories can be illustrated in the standard Lee model, in particular fixed point theorems and superconvergency. The problem of equal time commutator has also been discussed. All “physical” results, both for the smeared and for the point source model depend on well defined and calculable quantities, the high energy behaviour of the scattering amplitude being in agreement with Bjorken's theorem. There is a particular “relativistic” generalisation of the model which allows for PCAC.