Non-linear superposition law and Skyrme crystals
Abstract
Exact configurations of the four dimensional Skyrme model are presented. The static configurations have the profile which behaves as a kink and, consequently, the corresponding energy momentum tensor describes a domain wall. Furthermore, a class of exact time periodic Skyrmions is discovered. Within such class, it is possible to disclose a remarkable phenomenon which is a genuine effect of the Skyrme term. For a special value of the frequency the Skyrmions admit a non linear superposition principle. One can combine two or more exact elementary Skyrmions (which may depend in a non trivial way on all the space like coordinates) into a new exact composite Skyrmion. Due to such superposition law, despite the explicit presence of non linear effects in the energy momentum tensor, the interaction energy between the elementary Skyrmions can be computed exactly. The relations with the appearance of Skyrme crystals is discussed.
Keywords
Cite
@article{arxiv.1307.0211,
title = {Non-linear superposition law and Skyrme crystals},
author = {Fabrizio Canfora},
journal= {arXiv preprint arXiv:1307.0211},
year = {2014}
}
Comments
13 pages, no figure. A discussion of the domain-wall behaviour of the static configurations has been included. A detailed analysis of the boundary conditions has been added. Version accepted for publication on Phys. Rev. D