Current conservation in electrodisintegration of a bound system in the Bethe-Salpeter approach

TL;DR

This paper calculates electromagnetic transition form factors for electrodisintegration of a bound system using the Bethe-Salpeter approach, emphasizing gauge invariance and current conservation.

Contribution

It demonstrates the importance of consistent Bethe-Salpeter amplitudes and current operators for accurate, gauge-invariant transition form factors in electrodisintegration.

Findings

Plane wave and final state interaction contributions cancel for all momentum transfers.

Current conservation is achieved only with strictly consistent amplitudes and operators.

Reliable form factors require consistent Bethe-Salpeter solutions.

Abstract

Using our solutions of the Bethe-Salpeter equation with OBE kernel in Minkowski space both for the bound and scattering states, we calculate the transition form factors for electrodisintegration of the bound system which determine the electromagnetic current J of this process. Special emphasis is put on verifying the gauge invariance which should manifest itself in the current conservation. We find that for any value of the momentum transfer q the contributions of the plane wave and the final state interaction to the quantity J.q cancel each other thus providing J.q=0. However, this cancellation is obtained only if the initial Bethe-Salpeter amplitude (bound state), the final one (scattering state) and the current operator are strictly consistent with each other. A reliable result for the transition form factor can be found only in this case.