9 - Reggeization of an electron

Summary

In this lecture we shall continue to consider the perturbation theory of quantum electrodynamics with a photon with a non-zero mass λ. The conventional QED with λ = 0 has its own specific features, which will be addressed later.

The reason for considering this theory and for accounting for all complications related to spin, is that in the field theory with vector mesons one may expect the appearance of Regge particles at small values of the coupling constant g. We note that although in the gφ³ theory there is a Regge pole, it is situated not near j = 0, which is required for reggeization of a scalar particle, but near j = − 1. From the point of view of Feynman diagrams this is related to the fact that in the t-channel with a fixed momentum transfer we had two particles instead of one in the Born pole diagram. Each additional line in the t-channel reduces the asymptotics of a diagram by one power of the large variable s. A compensation of this suppression is possible owing to the Azimov spin shifting, which is made manifest by the appearance of the factor s^σ in the numerator of the Feynman amplitude, with σ the spin of the added particle. One can see from this that to make reggeization of a ‘nucleon’ possible in perturbation theory we should have a particle with σ = 1. Such a situation is realized in QED (see Fig. 9.1).