Diverse applications of the gauging of equations method

The gauging of equations method was developed some years ago in order to extract gauge invariant electromagnetic currents from strongly interacting few-body systems described by integral equations. Although the method is by now well-established for this purpose, it is not so well known that the same approach can be used to solve a wide variety of problems. The purpose of this paper is to demonstrate the true power of this method by using it to solve key problems in three very different areas of study; in particular, we show (i) how generalized parton distributions (GPDs) can be determined in the case where hadrons are described in terms of their partonic degrees of freedom through solutions of dynamical equations, (ii) how to construct gauge invariant two-nucleon currents in cutoff effective field theory (EFT), even though the cutoff usually violates the gauge invariance of the underlying Lagrangian, and (iii) how to construct a potential model of πN scattering that is crossing symmetric and approximately unitary. It is noteworthy that in each case, the gauging of equations method produces results that are consistent with the relevant requirements of quantum field theory. For example, in extracting GPDs from the model of strong interactions defined by dynamical equations, all possible mechanisms contributing to the GPDs are taken into account, so that all GPD sum rules are satisfied automatically. Similarly, in the construction of electromagnetic currents in cutoff EFT, gauge invariance is a consequence of the fact that an external photon is effectively coupled to every part of every strong interaction diagram in the model.