Towards Gauge theory for a class of commutative and non-associative fuzzy spaces | Zendy

Sanjaye Ramgoolam | Zendy

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Towards Gauge theory for a class of commutative and non-associative fuzzy spaces

Author(s) -

Sanjaye Ramgoolam

Publication year - 2004

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 - 10.1088/1126-6708/2004/03/034

Subject(s) - associative property , brst quantization , gauge covariant derivative , introduction to gauge theory , covariant transformation , gauge theory , mathematics , supersymmetric gauge theory , pure mathematics , commutative property , gauge anomaly , algebra over a field , physics , mathematical physics

We discuss gauge theories for commutative but non-associative algebrasrelated to the $ SO(2k+1)$ covariant finite dimensional fuzzy $2k$-spherealgebras. A consequence of non-associativity is that gauge fields and gaugeparameters have to be generalized to be functions of coordinates as well asderivatives. The usual gauge fields depending on coordinates only are recoveredafter a partial gauge fixing.The deformation parameter for these commutativebut non-associative algebras is a scalar of the rotation group. This suggestsinteresting string-inspired algebraic deformations of spacetime which preserveLorentz-invariance.Comment: 34 pages ; v2, v3- minor typos fixe

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