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Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

Brian P. Dolan·Idrish Huet·Sean Murray·Denjoe O'Connor
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Abstract

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.

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Brian P. Dolan, Idrish Huet, Sean Murray, Denjoe O'Connor. 2008-09-09. Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives. https://doi.org/10.1088/1126-6708%2F2007%2F07%2F007

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