Excited Kinks as Quantum States

Abstract

At one loop, quantum kinks are described by a sum of quantum harmonic oscillator Hamiltonians, and so their spectra are known exactly. We find the first correction beyond one loop to the quantum states corresponding to kinks with an excited bound or unbound normal mode, and also the corresponding two-loop correction to the energy cost of exciting the normal mode. In the case of unbound normal modes, this correction is equal to sum of the corresponding nonrelativistic kinetic energy plus the usual one-loop correction to the mass of the corresponding plane wave in the absence of a kink. We also sketch a diagrammatic method for such calculations.

Kink Form Factors

“…[13] while the corresponding states for excited kinks were given in Ref. [15]. The center of mass motion was considered in Ref.…”

“…Nonetheless, for problems such as finding the energy spectrum, this light-weight method is sufficient. So far this linearized soliton sector perturbation theory has been used to calculate the two-loop masses of kink ground states [13,14], the leading corrections to the energy required to excite kink shape modes and continuum excitations [15] and the instantaneous acceleration of a kink in the presence of an impurity [16]. For this last calculation, it was necessary to consider the full position-dependence of the kink wave function.…”

Form factors for meson-kink scattering

“…Recently, we have begun a systematic treatment of such processes, as an expansion in the coupling g. The order O(g 0 ) scattering, corresponding to classical wave mechanics, was treated in Ref. [22].…”

“…Although the generalization is straightforward [22], in this paper we consider classically reflectionless kinks, such as those in the Sine-Gordon and φ 4 double-well models, for concreteness. For these, we fix the sign of k such that g * k (x) = g −k (x) and, for |x| 0, g k (x) is proportional to e −ikx .…”

Kink form factors

“…So far this linearized soliton sector perturbation theory has been used to calculate the two-loop masses of kink ground states [13,14], the leading corrections to the energy required to excite kink shape modes and continuum excitations [15] and the instantaneous acceleration of a kink in the presence of an impurity [16]. For this last calculation, it was necessary to consider the full position-dependence of the kink wave function.…”