Meson production from kink-meson scattering

Form factors for meson-kink scattering

“…In contrast, since H (L) does not commute with the momentum operator, an exact eigenstate of H (L) , as proposed in Ref. [23], would not be translation invariant. We have now avoided this problem by adding corrections to the H (L) eigenstate which are exponentially suppressed in mx 0 .…”

“…(6.4) of Ref. [23]. In that reference they were found by simply replacing the normal modes with plane waves and removing the terms localized near the kink.…”

“…Next an exhaustive treatment of scattering processes with probabilities of order O(g 2 ) was performed. There are only three processes, meson multiplication [23], in which the final state consists of two mesons and a kink, and (anti)-Stokes scattering [24], in which the final state consists of a single meson and a kink but an internal kink excitation is toggled. Meson multiplication was treated by evolving an incoming wave packet in Ref.…”

“…Meson multiplication was treated by evolving an incoming wave packet in Ref. [23] and by beginning with a full Hamiltonian eigenstate in Ref. [25], reflecting the two strategies in nonrelativistic quantum mechanics described above.…”

“…The results here justify some assumptions made in Refs. [23,25,24] regarding quantum corrections to the initial and final states in inelastic meson-kink scattering. In the short term, this was the last missing ingredient needed for the study of several problems.…”