Elastic Kink-Meson Scattering

In classical field theory, radiation does not reflect off of reflectionless kinks. In quantum field theory, radiation quanta, called mesons, can be reflected. We provide a general analytical formula for the leading order amplitude and probability for the elastic scattering of mesons off of reflectionless quantum kinks. In the case of the Sine-Gordon model we verify that, due to a cancellation of six contributing processes, our general formula yields an amplitude of zero, as is required by integrability.