Possible disappearance of quantum-field divergences within the framework of modified quantum dynamics

Abstract

The paper considers the possible difference between the results given by ordinary quantum dynamics and the modified quantum dynamics presented in an earlier paper [1] when microprocesses are described. It is shown that in the case of a system of weakly interacting particles both theories should lead to substantially different results in situations in which intermediate states with very high energies appear in the relevant perturbation series. A situation of this kind obtains primarily in models of quantum field theory with a local interaction, in which the energy of the intermediate states is in general unlimited; as a result there are the familiar problems with divergences. The semirelativistic model of two interacting scalar fields is used as an example to show that these difficulties do not arise within the framework of the modified quantum dynamics.