TL;DR
This paper extends a linearized perturbation theory for quantum solitons to construct moving kink states and wave packets, enabling the study of their dynamics and properties beyond stationary solutions.
Contribution
It develops a method to create normalizable moving kink wave packets within an existing linearized perturbation framework, overcoming previous limitations to stationary solitons.
Findings
Constructed nonnormalizable kink states with fixed nonzero momentum.
Built localized, normalizable kink wave packets moving along classical trajectories.
Calculated matrix elements to analyze wave packet properties.
Abstract
Recently a linearized perturbation theory has been formulated for soliton sectors of quantum field theories. While it is more economical than alternative formalisms, such as collective coordinates, it is currently limited to solitons which stay close to a base point, about which the theory is linearized. As a result, so far this formalism has only been applied to stationary solitons. In spite of this limitation, we construct kink states with fixed nonzero momenta and also moving, normalizable kink wave packets. The former are nonnormalizable, coherent superpositions of kinks at all spatial positions and are simultaneous eigenstates of the Hamiltonian and the momentum operator. The latter are localized about a single, moving classical solution. To understand the wave packets, we calculate several simple matrix elements.
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