Gauge theory on nonassociative spaces
Majid, S.
arXiv, 0506453 / Harvested from arXiv
Text on arXiv
We show how to do gauge theory on the octonions and other nonassociative algebras such as `fuzzy $R^4$' 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 usual gauge theory on the underlying classical space. We give a general U(1)-Yang-Mills example for any quasi-algebra and a full description of the moduli space of flat connections in this theory for the cube $Z_2^3$ and hence for the octonions. We also obtain further results about the octonions themselves; an explicit Moyal-product description of them as a nonassociative quantisation of functions on the cube, and a characterisation of their cochain twist as invariant under Fourier transform.
Publié le : 2005-06-22
Classification:  Mathematics - Quantum Algebra,  High Energy Physics - Theory,  Mathematical Physics,  Mathematics - Category Theory 
@article{0506453,
     author = {Majid, S.},
     title = {Gauge theory on nonassociative spaces},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506453}
}

Majid, S. Gauge theory on nonassociative spaces. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506453/