Types of quantum field thories
The probability amplitude for a process of scattering of fundamental particles or fundamental strings off each other. The collection of scattering amplitudes forms the S-matrix. In perturbation theory this is computed by the Feynman diagram perturbation series.
A good text is
bridge the gap between a standard course in quantum field theory and recent fascinating developments in the studies of on-shell scattering amplitudes.
A historical overview of the development of on-shell methods/analytic methods is in
Ruth Britto, Loop amplitudes in gauge theories: modern analytic approaches (arXiv:1012.4493)
In super Yang-Mills theory (and there in particular in the planar limit of N=4 D=4 super Yang-Mills theory) scattering amplitudes enjoy special symmetry properties, some of which can be used to extract information about scattering amplitudes in non-supersymmetric theories (see also at amplituhedron):
Wieland Staessens, Bert Vercnocke, Lectures on Scattering Amplitudes in String Theory (arXiv:1011.0456)
For more see at string scattering amplitude.
Motivic structures in scattering amplitudes (see at motives in physics) are discussed for instance in
See also the references at period.