Thomas Schucker

Moyal Planes are Spectral Triples

Axioms for nonunital spectral triples, extending those introduced in the unital case by Connes, are proposed. As a guide, and for the sake of their importance in noncommutative quantum field theory, the spaces R2N endowed with Moyal products are intensively investigated. Some physical applications, such as the construction of noncommutative Wick monomials and the computation of the Connes–Lott functional action, are given for these noncommutative hyperplanes.

Connes' model building kit

Abstract A. Connes and J. Lotts applications of non-commutative geometry to interaction physics are described for the purpose of model building.

On the universal Chamseddine–Connes action. I. Details of the action computation

We give a detailed computation of the bosonic action of the Chamseddine–Connes model which we performed using different techniques.

Yang-Mills-Higgs versus Connes-Lott

By a suitable choice of variables we show that every Connes-Lott model is a Yang-Mills-Higgs model. The contrary is far from being true. Necessary conditions are given. Our analysis is pedestrian and illustrated by examples.

The standard model à la Connes-Lott

Abstract The relations among coupling constants and masses in the standard model a la Connes-Lott with general scalar product are computed in detail. We find a relation between the top and the Higgs masses. For mt = 174 ± 22 GeV it yields mH = 277 ± 40 GeV. The Connes-Lott theory privileges the masses mt = 160.4 GeV and 251.8 GeV.

Fuzzy Mass Relations for the Higgs

The noncommutative approach of the standard model produces a relation between the top and the Higgs masses. We show that, for a given top mass, the Higgs mass is constrained to lie in an interval. The length of this interval is of the order of m2τ/mt.

The noncommutative constraints on the standard model à la Connes

Noncommutative geometry applied to the standard model of electroweak and strong interactions was shown to produce fuzzy relations among masses and gauge couplings. We refine these relations and show then that they are exhaustive.

A left-right symmetric model à la Connes-Lott

We present a left-right symmetric model with the gauge group U(2)L × U(2)R within the Connes-Lott noncommutative framework. Its gauge symmetry is spontaneously broken, although parity remains unbroken.

Strong lensing in the Einstein–Straus solution

We analyse strong lensing in the Einstein–Straus solution with positive cosmological constant. Our result confirms Rindler and Ishak’s finding that a positive cosmological constant decreases the bending of light by an isolated spherical mass. In agreement with an analysis by Ishak et al., this decrease is found to be attenuated by a homogeneous mass distribution added around the spherical mass and by a recession of the observer. For concreteness we compare the theory to the light deflection of the lensed quasar SDSS J1004+4112.We analyse strong lensing in the Einstein–Straus solution with positive cosmological constant. Our result confirms Rindler and Ishak’s finding that a positive cosmological constant decreases the bending of light by an isolated spherical mass. In agreement with an analysis by Ishak et al., this decrease is found to be attenuated by a homogeneous mass distribution added around the spherical mass and by a recession of the observer. For concreteness we compare the theory to the light deflection of the lensed quasar SDSS J1004+4112.

Noncommutative geometry beyond the standard model

A natural extension of the standard model within noncommutative geometry is presented. The geometry determines its Higgs sector. This determination is fuzzy, but precise enough to be incompatible with experiment.