A covariant formulation of the non-adiabatic method for the relativistic two-body problem (II)

Abstract

It has been shown in Part I of this work how the Tamm-Dancoff non adiabatic treatment of the relativistic problem of two particles interacting through a neutral pseudoscalar meson field can be put in a covariant form. The integral equations obtained involve infinite kernels corresponding to radiative processes. In the present Part II the techniques of Dyson and Matthews for the renormalization of theS-matrix have been applied in order to separate from the kernel of the integral equations a convergent part, showing that the divergent contributions can be absorbed in unobservable mass and coupling constant renormalization. If we assume the normalized masses and charge to be defined by the same formal series with divergent constant terms as in theS-matrix, as required if a physical meaning is to be attached to the renormalization procedure, finite contributions arise also from self energy kernels of non interacting particles. The terms arising from disconnected loops in the vacuum can be eliminated if the same approximation is used as in the (S-matrix theory, namely that the time dependence of the state vector can be neglected in these integrals.