We present a unified description of the relativistic $\pi \mathrm{NN}$ and $\gamma \pi \mathrm{NN}$ 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 $N\overrightarrow{N}NN,\hspace{0.5em}N\overrightarrow{N}\pi d,\hspace{0.5em}\pi \overrightarrow{d}\pi d,$ etc. and corresponding electromagnetic processes $N\overrightarrow{N}\gamma NN,$ $\gamma \overrightarrow{d}NN,$ $\gamma d$ $\to \pi d,$ $e\overrightarrow{d}ed,$ $e\overrightarrow{d}{e}^{\prime }\pi d,$ 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 $\pi \mathrm{NN}-\mathrm{like}$ systems. The unified description is achieved through the use of the recently introduced gauging of equations method.

• Received 12 October 1998

DOI:https://doi.org/10.1103/PhysRevC.59.1263