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The massive gauge field, either free or coupled to a massless fermion field, is shown to be the Lagrangian equivalent of a composite massless field containing pseudoscalar as well as vector components. These fields are minimally coupled to each other while the pseudoscalar part has no direct fermion interaction (vector dominance). In general the total boson field consists of both vector and pseudoscalar components, but there exists a privileged gauge in which the pseudoscalar components are transformed away. The vector field in this special gauge is formally identical to the pseudoscalar current in the general gauge; therefore the field algebra in the privileged gauge is identical to the current algebra in the general gauge. That is, vector fields go into pseudoscalar currents under a local gauge transformation. In the formalism the pseudoscalar field plays the role of a coordinate system on the group space while the vector field correlates the group space at distinct space-time points. The nonlinear Lagrangian may be expressed in terms of geometric invariants of the group space and is manifestly invariant under general transformation of the pseudoscalar field.