On the Cut-off Theory in Quantum Field Theory

Abstract

For the investigation of the problem of internal consistency of current quantum field theory the cut-off method is usually adopted. Among others, the cut-off method proposed by Gell-Mann and Low has very frequently been used and was very useful for finding the high-energy behavior of quantum field theory. However, no one to this data has ever made certain whether this cut-off method was really a consistent cut-off theory, or whether it reduced to the original divergent theory in the nomenclature of Gell-Mann and Low when the cut-off momentum was made to go to infinity. In this note this problem in Lee's model and up to the fourthorder perturbation approximations in quantum electrodynamics is considered. (A.C.)