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A Remark on the Use of Differential Forms for the Skyrme Problem
Authors:Tristan Rivière
Affiliation:(1) Centre de Mathématiques et de Leurs Applications, CNRS, URA 1611, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France
Abstract:We introduce a formulation of the Skyrme problem using differential forms. By means of this formulation, we prove first that the homothetic map between the standard three-sphere of radius R, S3r sub R4, and S31 is the unique minimizer, modulo isometries, of the Skyrme energy in its homotopy class, for any R less than some critical value R0 isin (radic3/2, radic2]. We then establish a stability result for this Skyrme-form problem from which we can recover the result of M. Loss and N. S. Manton which states that this homothetic map is stable only up to R = radic2.
Keywords:calculus of variations  skyrme energy particle physics  skyrmion non-linear partial differential equations.
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