Graphical representation of CPT

Abstract

In any quantum mechanical collision process we are interested in computing the amplitude or the matrix element for a transition from an initial system of particles to a final system of particles. In Feynman perturbation theory, these represent the external lines of the Feynman diagram. Perturbation theory implies that these external lines are either connected directly with one another or through propagators, which are off the energy shell. Thus, while the fourth component of the four momenta of the particles representing the external lines are just the energies computed by the relativistic relation between energy and momentum in the case of the propagators this need not be the case. So, if symmetry operations dealing with energy and momentum are defined for free particles, it is not clear how they can be carried over to the propagators. In particular it is not apparent at first sight how an operation switching particles to antiparticles affects the propagator which is characterized only by a single parameter representing the four momentum. However if we decompose the propagators into positive and negative energy parts, we have shown in the previous contribution [1] that the particles are on the energy shell and thus the symmetry operations on free particles can be taken over directly to all orders of perturbation. Thus it suffices to define the operation of CPT for only free particles in Feynman graphical formalism and demonstrate how it can straightaway be carried over to interacting fields.