scholarly journals The Standard Model Fermion Spectrum From Complex Projective Spaces

2002 ◽  
Vol 2002 (10) ◽  
pp. 041-041 ◽  
Author(s):  
Brian P Dolan ◽  
C Nash
Keyword(s):  
Standard Model ◽  
Projective Spaces ◽  
Standard Model Fermion ◽  
Complex Projective Spaces ◽  
The Standard Model ◽  
Complex Projective

scholarly journals NON-COMMUTATIVE COMPLEX PROJECTIVE SPACES AND THE STANDARD MODEL

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2319-2327 ◽  
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Standard Model ◽  
Projective Spaces ◽  
Yukawa Couplings ◽  
Complex Spaces ◽  
Complex Dimension ◽  
Complex Projective Spaces ◽  
Fuzzy Space ◽  
The Standard Model ◽  
Complex Projective ◽  
Higgs Fields

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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