In this chapter, we discuss the S-matrix theory in quantum field theory.
Here, we first treat the non-relativistic scattering theory and its relation to the Tmatrix.
In particular, we discuss the scattering problem in terms of the Lippmann-
Schwinger equation. Then we discuss the S-matrix theory in quantum field theory.
This is based on the perturbation theory and we present the example of the S-matrix
evaluation. In particular, we discuss some basic problems in the Feynman propagator
of photon and show a possible physical difference between Feynman and correct
propagators of photon.
Keywords: S-matrix, T-matrix, scattering amplitude, Lippmann-Schwinger equation,
time-dependent perturbation theory, Born approximation, cross section, Feynman and
correct propagator of photon.