The off-shell behavior of the current amplitude is studied in the framework of a field -theoretical model of vector-meson dominance based on the spontaneously broken gauge theory. We discuss mainly thc effects of the Higgs scalar mesons, in particular the implications of a straightforward modification of the ordinary algebra of fields. The Schwinger term, which depends on the Higgs scalars, and some of the Schwinger-term sum rules are briefly discussed. The ratio R in the deep-inelastic process and the Callan-Gross relation are discussed in detail based on a simple model. Our result suggests that the longitudinal component is still logarithmically enhanced relative to the transverse component. The renomalizability and the enhancement of the longitudinal component are therefore independent properties. It is also emphasized that the ratio R, given by the dispersive approach a vector dominance, is logically independent of the large ratio R required by the algebra of fields. The effects of the Higgs scalars on electron-positron annihilation are also compared with those of the dilation; the annihilation cross section scales up to logarithmic factors. We note that the naive scale dimension of the current and Bjorken scaling (or scaling in the annihilation process) have very little to do withmore » each other in the present approach. We also note that in the ordinary perturbative sense the lepton current couples to a nonconserved piece of the hadron source current. The implication of this property for the construction of the dual current amplitude is discussed. The extension of the model to include many vector mesons is also commented on. (auth)« less