The mass of gauge particles and the self-consistent method of quantum field theory

Abstract

The aim of the present paper is to apply the self-consistent method based on inequivalent representations, which was developed in our previous papers, to vector fields in order to see whether the so-called gauge theories can allow nonzero masses for gauge vector fields. The Stueckelberg formalism is exclusively used, which is most convenient for our present purpose. It is shown that the representations for vector fields with nonzero mass are inequivalent to those for vector fields with zero mass even when the cut-off momentum and the normalization volume are finite. In quantum electrodynamics it can be shown that the photon cannot have any stable sister particle with nonzero mass. However, it is possible that there exists such a sister particle which is unstable. Our consideration is further extended to the Yang-Mills field as a simple example of multiplet gauge fields. It can be shown that the three components of this field cannot have an equal, nonzero mass simultaneously, but that they can have nonzero masses in an asymmetric way such that at least one of the three masses is different from the others. Most conclusions reached here seem to be valid in more general cases of gauge theories.