Gauging of equations method. I. Electromagnetic currents of three distinguishable particles

Abstract

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.

Nucleon electromagnetic form factors from the covariant Faddeev equation

“…(18) to the underlying description of the nucleon as a composite object, one must specify how a photon couples to its constituents. A systematic construction principle for the nucleon-photon current based on electromagnetic gauge invariance is the ''gauging of equations'' prescription [72][73][74] which was previously used to derive the electromagnetic current in the quark-diquark model [42,75]. We will briefly sketch the procedure here.…”

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…”

Implementing PCAC in Nonperturbative Models of Pion Production

“…Until recently, however, what has not been known is the way to achieve this complete coupling for a few-body system whose strong interactions are described nonperturbatively by integral equations. Fortunately, the solution to this problem presented recently in the context of electromagnetic interactions [1,2], is based on a topological argument and therefore applies equally well to the present case of an axial vector field.…”