Bilocal Formalism in Quantum Field Theory
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  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  have gone a long way to solving the problem of constructing a computational scheme — that is, a modified perturbation theory  for finding the Green’s functions and cross sections — that substantially extends the scope of ordinary perturbation theory.
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