Some topological issues for ferromagnets and fluids |
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| Institution: | 1. Physics Department, City College of the CUNY, New York, NY 10031, USA;2. Physical Review Letters, American Physical Society, Ridge, NY 11367, USA;1. Department of Mathematics, Jinan University, Guangzhou 510632, China;2. Department of Optoelectronic Engineering, Jinan University, Guangzhou 510632, China;1. Departamento de Matemáticas, CINVESTAV, Apartado Postal 14-740, C.P. 07000, México, D.F., Mexico;2. Departamento de Matemáticas, Universidad de los Andes, Carrera 1 N. 18A - 10, Bogotá, Colombia;3. Departamento de Matemáticas y Estadística, Universidad del Norte, Km 5 via Puerto Colombia, Barranquilla, Colombia |
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| Abstract: | We analyze the canonical structure of a continuum model of ferromagnets and clarify known difficulties in defining a momentum density. The moments of the momentum density corresponding to volume-preserving coordinate transformations can be defined, but a nonsingular definition of the other moments requires an enlargement of the phase space which illuminates a close relation to fluid mechanics. We also discuss the nontrivial connectivity of the phase space for two and three dimensions and show how this feature can be incorporated in the quantum theory, working out the two-dimensional case in some detail. |
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