Abstract
We show that the leading semiclassical behavior of soliton form factors at arbitrary momentum transfer is controlled by solutions to a new wavelike integro-differential equation that describes solitons undergoing acceleration. We work in the context of two-dimensional linear σ models with kink solitons for concreteness, but our methods are purely semiclassical and generalizable.
Highlights
CRST and School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
We work in the context of two-dimensional linear σ models with kink solitons for concreteness, but our methods are purely semiclassical and generalizable
Introduction.—Solitons feature prominently in quantum field theories relevant to our current understanding of nature: the Abrikosov and Nielsen-Olesen vortices in the theories of superconductors [1] and dual strings [2], baryons in the Skyrme model of nucleonic interactions [3], and magnetic monopoles in grand unified theories [4,5]
Summary
We show that the leading semiclassical behavior of soliton form factors at arbitrary momentum transfer is controlled by solutions to a new wavelike integro-differential equation that describes solitons undergoing acceleration. The kink is a time-independent energy-minimizing solution to the equations of motion, φ 1⁄4 φ0ðxÞ, that interpolates between two distinct minima as x → Æ∞ These disjoint sectors in the space of finite-energy field configurations lead to orthogonal sectors of the Hilbert space of quantum states, and a classical soliton solution corresponds to a one-particle state in a topologically nontrivial sector [6]. The leading semiclassical behavior of this form factor for generic momentum transfer, k ≡ Pf − Pi, is not known in nonintegrable models.
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