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

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

2006-11-20

arxiv.org/abs/hep-th/0611209v2

JHEP0707:007,2007

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, v2 contains minor corrections to the published version

Scientific paper

10.1088/1126-6708/2007/07/007

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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