Bilocal Formalism in Quantum Field Theory

Abstract

In recent years wide use has been made of the functional method in quantum field theory to construct not only the S matrix in complicated nonlinear interactions but also to set up a computational scheme that is independent of perturbation theory. The adequacy of this method for describing systems with infinitely many degrees of freedom — and it is these systems we are concerned with in modern quantum field theory — has made it possible to obtain a solution for the S matrix (and for the generating functional of all the Green’s functions) of interacting fields in the most compact form possible. This operator (functional) solution [1] is expressed in terms of functional derivatives with respect to the local sources of Bose or Fermi fields or as a functional integral over local dynamical variables (over the “classical” fields). The operator solution for the S matrix and the operator (functional) solution for the Green’s function in an arbitrary external field obtained in [2] have gone a long way to solving the problem of constructing a computational scheme — that is, a modified perturbation theory [2] for finding the Green’s functions and cross sections — that substantially extends the scope of ordinary perturbation theory.