O(3) Sigma model with Hopf term on Fuzzy Sphere

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We formulate the O(3) - model on fuzzy sphere and construct the Hopf term. We show that the field can be expanded in terms of the ladder operators of Holstein-Primakoff realisation of SU(2) algebra and the corresponding basis set can be classified into different topological sectors by the magnetic quantum numbers. We obtain topological charge Q and show that -2j≤ Q ≤2j. We also construct BPS solitons. Using the covariantly conserved current, we construct the Hopf term and show that its value is Q² as in the commutative case. We also point out the interesting relation of physical space to deformed SU(2) algebra.