Gauging of equations method. II. Electromagnetic currents of three identical particles

Abstract

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.

Baryons as relativistic three-quark bound states

“…Fortunately, such a course is also not necessary because it is possible to derive an expression for the current matrix element The basic observation is that G [µ] is obtained from the six-point function G by insertion of an external current j [µ] (z). In the path-integral language this amounts to a functional derivative, which entails that the current couples linearly to all diagrams that appear in G. In that way the operation G → G [µ] carries the properties of a derivative, i.e., it is linear and satisfies the Leibniz rule, which is referred to as 'gauging of equations' [430][431][432][433]. Hence we can formally write…”

Two-photon decays of hadronic molecules

“…For scattering amplitudes similar formalisms were discussed in Refs. [16,17,18]. The relevant equations in the two limiting cases A and B introduced above will appear as special cases of these general equations.…”

Generalized parton distributions for dynamical equation models

“…Indeed the gauging method used in this paper is closely based on the one developed for the (n + 1)-point function of Eq. (7) [15,16,17,18].…”

“…In the 'gauging of equations method', the (n + 1)-point Green function G µ is obtained by 'gauging' Eq. (8) with a local (vector) field as [15,16,17,18] …”

“…Here, of course, the currents had to obey charge and current conservation. The solution to this problem came with the development of the 'gauging of equations method' [13,14,15,16,17,18]. This method not only solves the problem of extracting charge and current conserving electromagnetic currents, but it does so in accordance with strict adherence to theory: the external electromagnetic field is attached to all possible places in the nonperturbative strong interaction processes defined by the dynamic equation model.…”