Minimal substitution for isospin dependent potentials

The minimal substitution, p→p-qA, in the Hamiltonian operator of a nuclear system is a familiar method of introducing electromagnetic interactions in a gauge invariant way. The procedure does not work, however, when isospin dependent forces are present. In this work, the procedure is extended to isospin dependent potentials in a model-independent way. The ambiguity inherent in the minimal substitution is avoided by making a simple choice. The result is generally not expected to coincide with the predictions of a fundamental theory, if any, that may underlie the phenomenological nuclear potential, nor is it expected to resolve the present discrepancies between theory and experiment. Yet it is thought to be an improvement over treatments that ignore the so-called exchange and interaction currents altogether or treat them in an inconsistent or non-gauge-invariant manner. More general formulas containing arbitrary paths or functions are also given, as is a generalization that allows non-point-like nucleons. An application of the method to the photodisintegration of the deuteron is under way