Interaction of isotopic gauge fields with photons

Abstract

The quantization of the following systems of interacting fields is studied: i) Yang-Mills isotopic gauge field interacting with the electromagnetic field; ii) partially isotopic gauge-invariant field (with nonvanishing mass terms and arbitrary anomalous moment type couplings); and iii) its interaction with the electromagnetic field (with arbitrary anomalous magnetic moment couplings). By assuming the isotopic charge to be small, the perturbativeS-matrix theory is formulated for each of the three problems. The field system i) is renormalizable, but ii) and iii) are not. The interaction with the electromagnetic field by consistent couplings does not completely destroy the isotopic gauge invariance of the Yang-Mills field, but rather leads to an extended invariance of the whole system of two interacting fields with respect to a 4-dimensional gauge group called the combined charge-isotopic gauge group, which can still be generalized to include any number of kinds of « photons ». This extended gauge invariance enables us to take Lorentz gauge for both the electromagnetic and the isotopic gauge-invariant field and also permits a global covariant formalism for dealing with the subsidiary conditions of all the component zero-mass vector fields. In both problems ii) and iii), all anomalous moment interactions give rise to noncovariant high-orderS-matrix elements and to « extra-high-order » divergences, but these difficulties all disappear in a certain particular case; the results of the two problems may be applied to analysing the interaction among charged and neutral vector mesons of isospin one considered as isotopic gauge bosons and also their interaction with photons.