A Remark on the Use of Differential Forms for the Skyrme Problem |
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Authors: | Tristan Rivière |
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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 |
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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 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 (3/2, 2]. 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 = 2. |
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Keywords: | calculus of variations skyrme energy particle physics skyrmion non-linear partial differential equations. |
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