Non-commutative Complex Projective Spaces And The Standard Model
Dolan, Brian P. (2003) Non-commutative Complex Projective Spaces And The Standard Model. Modern Physics Letters A, 18 (33-35). pp. 2319-2327. ISSN 0217-7323
The standard model fermion spectrum, including a right handed neutrino, can be obtained as a zeremode 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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