Non-commutative Complex Projective Spaces and the Standard Model
摘要
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.
引用
@article{arxiv.hep-th/0307124,
title = {Non-commutative Complex Projective Spaces and the Standard Model},
author = {Brian P. Dolan},
journal= {arXiv preprint arXiv:hep-th/0307124},
year = {2009}
}
备注
Contribution to conference in honour of A.P. Balachandran's 65th birthday: "Space-time and Fundamental Interactions: Quantum Aspects", Vietri sul Mare, Italy, 25th-31st May, 2003, 10 pages, typset in LaTeX