  This paper extends the study, initiated by Rozowsky and Thorn [1], of gauge
fields in interaction with Dirac fields living on separated parallel 1-branes.
In a lightcone description, replacing static point sources by 1-brane sources
allows p^+ conservation to be maintained in their presence, which simplifies
the lightcone quantization procedure. Here we calculate on-shell branion
scattering amplitudes through 1 loop in lightcone gauge, and thereby resolve a
puzzling ambiguity encountered in the off-shell calculations of [1]. We confirm
that infrared divergences cancel in properly defined scattering probabilities.
This work lays the groundwork for the incorporation of 1-brane sources in the
lightcone worldsheet formalism.
