Unified relativistic description of πNN and γπNN

We present a unified description of the relativistic πNN and γπNN systems where the strong interactions are described nonperturbatively by four-dimensional integral equations. A feature of our approach is that the photon is coupled in all possible ways to the strong interaction contributions. Thus the hadronic processes NN⃗NN, NN⃗πd, πd⃗πd, etc. and corresponding electromagnetic processes NN⃗γNN, γd⃗NN, γd →πd, ed⃗ed, ed⃗e^′πd, etc., are described simultaneously within the one model of strong interactions. Our formulation obeys two and three-body unitarity, and as photons are coupled everywhere in the strong interaction model, gauge invariance is implemented in the way prescribed by quantum field theory. Our formulation is also free from the overcounting and undercounting problems plaguing four-dimensional descriptions of πNN-like systems. The unified description is achieved through the use of the recently introduced gauging of equations method.