Gauge theory on nonassociative spaces

Journal Article · Sat Oct 01 04:00:00 EDT 2005 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2084747· OSTI ID:20699520

Majid, S ^[1]

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1. School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Rd., London E1 4NS (United Kingdom)

We show how to do gauge theory on the octonions and other nonassociative algebras such as 'quasi-R{sup 4}' models proposed in string theory. We use the theory of quasialgebras obtained by cochain twist introduced previously. The gauge theory in this case is twisting-equivalent to the usual gauge theory on the underlying classical space. We give a general U(1)-Yang-Mills example for any quasialgebra and a full description of the moduli space of flat connections in this theory for the cube Z{sub 2}{sup 3} and hence for the octonions. We also obtain further results about the octonions themselves; an explicit Moyal-product description of them as a nonassociative quantization of functions on the cube, and a characterization of their cochain twist as invariant under Fourier transform.

• OSTI ID: 20699520
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 46; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
FOURIER TRANSFORMATION
FUNCTIONS
GAUGE INVARIANCE
MATHEMATICAL SPACE
QUANTIZATION
STRING MODELS
YANG-MILLS THEORY