Hui Liu

Classically, reflectionless kinks transmit all incident radiation. Recently, we have used an analyticity argument together with a solution of the Lippmann-Schwinger equation to write down the leading quantum correction to the reflection probability. The argument was fast, but rather indirect. In the present paper, we calculate the reflection coefficient and probability by methodically grinding through the Schrödinger picture time evolution. We find the same answer. This answer contains contributions not considered in the traditional calculation of meson-kink scattering in 1991. However, as a result of these contributions, our total result is zero in the case of the Sine-Gordon model, and so it is consistent with integrability. Published by the American Physical Society 2024

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.