Vortex-condensations of a non-relativistic Maxwell-Chern-Simons theory
The paper describes an elliptic system subject to boundary conditions arising from the study of vortex-condensates for a selfdual non-relativistic model introduced by \textit{G. Dunne} et al. [Phys. Rev. D. 43, 1332-1345 (1990)] in the framework of Chern-Simons gauge theory. The author proves the existence of a vortex-condensate for all possible values of the relevant physical parameters involved in the model and for every prescribed set of zeroes of the Higgs-scalar. Among other things there is proved that for every region the given system can accomodate any number of vortices even though they all carry charges of same sign. Uniqueness problems are discussed and developed also. In analogy with the classical vortex theory there is also shown that the zero-set of the Higgs scalar uniquely determines the corresponding solution provided that the mass \(m_A\) of the gauge field is suitably restricted (according to the prescribed zero-set), while the mass \(m\) of the Higgs field may be arbitrary.
scientific article; zbMATH DE number 1109513