Noncommutative vector bundles over fuzzy CPN and their covariant derivatives

Dolan, Brian P. and Huet, Idrish and Murray, Sean and O'Connor, Denjoe (2007) Noncommutative vector bundles over fuzzy CPN and their covariant derivatives. Journal of High Energy Physics, 07 (007). pp. 1-35. ISSN 1126-6708

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We generalise the construction of fuzzy CPN 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 S2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommutative 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
Additional Information: Preprint version of original published article. Published by Institute of Physics (doi:10.1088/1126-6708/2007/07/007). We have benefited from many discussions with our colleagues and would especially like to thank A.P. Balachandran, Charles Nash, Peter Presnajder and Christian Samann for their stimulating comments. The work has been supported by Enterprise Ireland grant SC/2003/0415.
Keywords: Discrete and Finite Symmetries; Solitons; Monopoles and Instantons; Matrix Models; Non-Commutative Geometry; Vector Bundles; Fuzzy;
Academic Unit: Faculty of Science and Engineering > Mathematical Physics
Item ID: 2838
Identification Number: 10.1088/1126-6708/2007/07/007
Depositing User: Dr. Brian Dolan
Date Deposited: 16 Nov 2011 16:37
Journal or Publication Title: Journal of High Energy Physics
Publisher: Institute of Physics
Refereed: No
Funders: Enterprise Ireland

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