Hopf term,fractional spin and soliton operators in the O(3) non-linear sigma model |
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| Affiliation: | 1. Institute for Cosmic Ray Research, University of Tokyo, Midori, Tanashi, Tokyo 188, Japan;2. Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Tanashi Branch, Midori, Tanashi, Tokyo 188, Japan;1. Key Laboratory of Beam Technology of the Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China;2. Institute of Radiation Technology, Beijing Academy of Science and Technology, Beijing 100875, China;1. Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China;2. Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium;3. Department WNI, University of Hasselt, Universitaire Campus, 3590 Diepenbeek, Belgium;1. Wigner Research Centre for Physics, H-1525 Budapest 114, P.O.B. 49, Hungary;2. Department of Mathematics, Macquarie University NSW 2109, Australia;1. CONICET, Argentina;2. Departamento de Matemática, FCEIA, Universidad Nacional de Rosario, Pellegrini 250, Rosario, Argentina |
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| Abstract: | We re-examine three issues, the Hopf term, fractional spin and the soliton operators, in the 2+1 dimensional O(3) non-linear sigma model based on the adjoint orbit parametrization (AOP) introduced earlier. It is shown that the Hopf term is well defined for configurations of any soliton charge Q if we adopt a time-independent boundary condition at spatial infinity. We then develop the Hamiltonian formulation of the model in the AOP and thereby argue that the well-known Q2 formula for fractional spin holds only for a restricted class of configurations. Operators that create states of given classical configurations of any soliton number in the (physical) Hilbert space are constructed. Our results clarify some of the points that are crucial for the above three topological issues and yet have remained obscure in the literature. |
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