Models of Electroweak Interactions in Non-Commutative Geometry: A Comparison

Abstract

Alain Connes' construction of the standard model is based on a generalized Dirac-Yukawa operator and the K-cycle $(\HD ,D)$, with $\HD$ a fermionic Hilbert space. If this construction is reformulated at the level of the differential algebra then a direct comparison with the alternative approach by the Marseille-Mainz group becomes possible. We do this for the case of the toy model based on the structure group $U(1)\times U(1)$ and for the $SU(2)\times U(1)$ of electroweak interactions. Connes' results are recovered without the somewhat disturbing ${\gamma }_5$-factors in the fermion mass terms and Yukawa couplings. We discuss both constructions in the same framework and, in particular, pinpoint the origin of the difference in the Higgs potential obtained by them.

9p, MZ-TH/93-26

References in corpus (3)

• Parameter restrictions in a non-commutative geometry model do not survive standard quantum corrections
• Differential Algebras in Non-Commutative Geometry
• Remarks on Alain Connes' approach to the standard model

Cited by in corpus (8)

• Connes' Model Building Kit
• Differential Algebras in Non-Commutative Geometry
• Noncommutative Kaluza-Klein Theory
• Non-commutative Geometry Beyond the Standard Model
• Fuzzy Mass Relations for the Higgs
• A Superconnection for Riemannian Gravity as Spontaneously Broken SL(4,R) Gauge Theory
• BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry
• Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra