Noncommutative vector bundles over fuzzy Bbb CBbb PNand their covariant derivatives | Zendy

Brian P. Dolan | Zendy; Idrish Huet | Zendy; Seán Murray | Zendy; Denjoe O’Connor | Zendy

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Noncommutative vector bundles over fuzzy Bbb CBbb P^Nand their covariant derivatives

Author(s) -

Brian P. Dolan,

Idrish Huet,

Seán Murray,

Denjoe O’Connor

Publication year - 2007

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2007/07/007

Subject(s) - noncommutative geometry , covariant transformation , vector bundle , mathematics , fuzzy logic , pure mathematics , algebra over a field , physics , mathematical physics , computer science , artificial intelligence

We generalise the construction of fuzzy CP^N in a manner that allows us toaccess all noncommutative equivariant complex vector bundles over this space.We give a simplified construction of polarization tensors on S^2 thatgeneralizes to complex projective space, identify Laplacians and naturalnoncommutative covariant derivative operators that map between the modules thatdescribe noncommuative sections. In the process we find a naturalgeneralization of the Schwinger-Jordan construction to su(n) and identifycomposite oscillators that obey a Heisenberg algebra on an appropriate Fockspace.Comment: 34 pages, v2 contains minor corrections to the published versio

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