Topological features of the nonlinear sigma model with Hopf term using chiral lagrangians |
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| Affiliation: | 1. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA;2. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;3. Department of Physics, Harvard University, Cambridge, MA 02138, USA;1. Université de Toulouse; UPS; Laboratoire de Physique Théorique; F-31062 Toulouse Cedex, France;2. CNRS; UMR5152; F-31062 Toulouse Cedex, France;3. Technological Research Institute IRT Saint Exupéry; F-31405 Toulouse Cedex 4, France;4. School of Mathematics and Physics, Queen''s University Belfast, Belfast, UK;5. Institut für Theoretische Physik, Universität Erlangen, Staudstrasse 7, D-91058 Erlangen, Germany;1. School of Mathematics and Physics, Bohai University, Jinzhou, China;2. QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland;1. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany;2. W. I. Fine Theoretical Physics Institute and School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA |
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| Abstract: | We rewrite the O(3) nonlinear sigma model in 2 + 1 dimensions in terms of SU(2) matrices, thereby solving the constraint. The lagrangian has the symmetry SU(2)Global×U(1)Local. Static soliton solutions to this lagrangian have energy 4πN as usual. We then show that the Hopf instantons, in the formalism of principle chiral fields, are just the skymions of QCD in 3 + 1 dimensions. |
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