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Non-abelian path integrals and generalised quantum mechanics in the external field of the 't Hooft-Polyakov monopole |
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| Institution: | Institute of Theoretical Physics, Hoża 69, Warsaw, Poland;Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Pohraniční 1288/1, 40501 Děčín, Czech Republic;Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University in Prague, Břehová 7, 11519 Prague, Czech Republic;Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland |
| Abstract: | By means of a “lagrangian” with values in the Lie algebra of some arbitrary Lie group we introduce a non-abelian path integral. For such generalised quantum mechanics we derive a non-abelian Schrödinger equation for the case of a particle in the 't Hooft-Polyakov monopole field. |
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