Covariant Perturbation Theory

Abstract

In the preceding chapter, the expressions for the vacuum-to-vacuum transition amplitude have been obtained. Of practical interest, however, are transitions of a system of initially free particles into a final system of free particles. As shown in Sect. 1.1, such transitions are described by the matrix elements of the S-matrix. Therefore, we shall find in this chapter an expression for the matrix element of the S-matrix, or for the transition amplitude between two states, in terms of the path integral. Unfortunately, effective general methods of analytic calculations of these integrals are lacking as yet and one has to resort to approximate ones. Most developed are the methods of perturbation theory representing the transition amplitude as a series in the coupling constant.