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arXiv · hep-th/0307124

Non-commutative Complex Projective Spaces and the Standard Model

Brian P. Dolan
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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.

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Brian P. Dolan. 2003-07-14. Non-commutative Complex Projective Spaces and the Standard Model. https://doi.org/10.1142/s0217732303012532

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