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

Dolan, Brian P. and Huet, Idrish and Murray, Seán and O'Connor, Denjoe (2006) Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives. Journal of High Energy Physics, 2007 (07). 007-007. ISSN 1029-8479

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Official URL: http://doi.org/10.1088/1126-6708/2007/07/007

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.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:31
Last Modified: 16 Jul 2018 10:38
URI: http://dair.dias.ie/id/eprint/182

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