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NON-COMMUTATIVE COMPLEX PROJECTIVE SPACES AND THE STANDARD MODEL

BRIAN P. DOLAN

Department of Mathematical Physics, National University of Ireland, Maynooth, Co. Kildare, Ireland

Dublin Institute for Advanced Studies, 10, Burlington Rd., Dublin, Ireland

https://doi.org/10.1142/S0217732303012532Cited by:2 (Source: Crossref)

Abstract

The standard model fermion spectrum, including a right handed neutrino, can be obtained as a zero-mode of the Dirac operator on a space which is the product of complex projective spaces of complex dimension two and three. The construction requires the introduction of topologically non-trivial background gauge fields. By borrowing from ideas in Connes' non-commutative geometry and making the complex spaces 'fuzzy' a matrix approximation to the fuzzy space allows for three generations to emerge. The generations are associated with three copies of space-time. Higgs' fields and Yukawa couplings can be accommodated in the usual way.

Keywords:

PACS: 11.10.Kk, 11.10.Nx, 11.25.Mj, 14.60.St

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