GAUGE-INVARIANCE AND THE ELECTROMAGNETIC CURRENT OF COMPOSITE PIONS

The Global Color-symmetry Model of QCD is extended to deal with a background electromagnetic held and the associated conserved current is identified for the finite size ($) over bar qq pion modes at tree level. We work within a well-defined truncation that factorizes the bilocal pion held into a local held variable and a hadronic form factor having a ladder Bethe-Salpeter content. The associated pion charge form factor is formulated. These developments are used to provide an illustration of how an effective hadronic action containing form factors may be electromagnetically coupled in a gauge invariant way that is accountable to its held substructure. In particular, the Ward-Takahashi identity for the photon vertex appropriate to the localized pion fields is seen to contain the hadronic form factors. In this context, gauge invariance of the effective hadronic action also requires recognition of the fact that the free inverse propagator for the localized pion held gauge transforms due to the substructure field content that has been absorbed into it.