We present a general method for incorporating an external electromagnetic field into descriptions of few-body systems whose strong interactions are described by integral equations. In particular, we address the case where the integral equations are those of quantum field theory and effectively sum up an infinite number of Feynman diagrams. The method involves the idea of gauging the integral equations themselves, and results in electromagnetic amplitudes where an external photon is effectively coupled to every part of every strong interaction diagram in the model. Current conservation is therefore implemented in the way prescribed by quantum field theory. We apply our gauging procedure to the four-dimensional integral equations describing a system of three distinguishable relativistic particles. In this way we obtain the expressions needed to calculate all possible electromagnetic processes of the three-body system. An interesting aspect of our results is the natural appearance of a subtraction term needed to avoid the overcounting of diagrams.
We derive relativistic three-dimensional integral equations describing the interaction of the three-nucleon system with an external electromagnetic field. Our equations are unitary, gauge invariant, and they conserve charge. This has been achieved by applying the recently introduced gauging of equations method to the three-nucleon spectator equations where spectator nucleons are always on mass shell. As a result, the external photon is attached to all possible places in the strong interaction model, so that current and charge conservation are implemented in the theoretically correct fashion. Explicit expressions are given for the three-nucleon bound state electromagnetic current, as well as the transition currents for the scattering processes γ 3 He→ NNN , N d → γN d, and γ 3 He→ N d. As a result, a unified covariant three-dimensional description of the NNN -γNNN system is achieved.
The gauging of equations method, introduced in the preceding paper, is applied to the four-dimensional integral equations describing the strong interactions of three identical relativistic particles. In this way we obtain gauge invariant expressions for all possible electromagnetic transition currents of the identical three-particle system. In the three-nucleon system with no isospin violation, for example, our expressions describe the electromagnetic form factors of 3 H, pd → pdγ, γ 3 He → pd, γ 3 He → ppn, etc. A feature of our approach is that gauge invariance is achieved through the coupling of the photon to all possible places in the (nonperturbative) strong interaction model. Moreover, once the proper identical particle symmetry is incorporated into the integral equations describing the strong interactions, the gauging procedure automatically provides electromagnetic transition currents with the proper symmetry. In this way the gauging of equations method results in a unified description of strong and electromagnetic interaction of strongly interacting systems.
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