First (fuzzy) Hopf map from irreps of SU(2) |
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| Authors: | Hossein Fakhri Mehdi Lotfizadeh |
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| Institution: | 1178. Department of Theoretical Physics and Astrophysics, Faculty of Physics, University of Tabriz, P. O. Box 51666-16471, Tabriz, Iran
2178. Department of Physics, Faculty of Science, Urmia University, P. O. Box 165, Urmia, Iran
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| Abstract: | Using the spherical basis of the spin-ν operator, together with an appropriate normalized complex (2ν +1)-spinor on S 3 we obtain spin-ν representation of the U(1) Hopf fibration S 3 → S 2 as well as its associated fuzzy version. Also, to realize the first Hopf map via the spherical basis of the spin-1 operator with even winding numbers, we present an appropriate normalized complex three-spinor. We put the winding numbers in one-to-one correspondence with the monopole charges corresponding to different associated complex vector bundles. |
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