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The flux of noncommutative U(1) instanton through the fuzzy spheres. (English) Zbl 1113.81102

Summary: From the ADHM construction on noncommutative \(\mathbb R_{\theta}^4\) vector space, we investigate different U(1) instanton solutions tied by partial isometry transformations. We recast these solutions under a form of vector fields in noncommutative \(\mathbb R_{\theta}^3\) vector space which makes possible the calculus of their fluxes through fuzzy spheres. For this end, we establish the noncommutative analog of Gauss theorem from which we show that the flux of the U(1) instantons through fuzzy spheres does not depend on the radius of these spheres and it is invariant under partial isometry transformations.

MSC:

81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
81T75 Noncommutative geometry methods in quantum field theory
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