arXiv subjects
Publications and source records attributed to Thomas Schucker.
We analyse strong lensing in the Einstein-Straus solution with positive cosmological constant. For concreteness we compare the theory to the light deflection of the lensed quasar SDSS J1004+4112.
On october 21st 1983 took place in Sèvres on the western outskirts of Paris the official funeral of the meter. With it the notion of distance as a physical observable was buried.
Strong lensing by an isolated spherically symmetric mass distribution is considered in presence of a positive cosmological constant. Deflection angles and time delay are computed and compared to the multiple image of the quasar SDSS J1004+4112.
The 1-loop corrections to the seesaw mechanism in the noncommutative standard model are computed. Other consequences of the Lorentzian signature in the inner space are summarised.
The effect of the cosmological constant on the time delay caused by an isolated spherical mass is calculated without using the lens equation and compared to a recent observational bound on the time delay of the lensed quasar SDSS J1004+4112.
The effect of the cosmological constant on the curvature of light due to an isolated spherical mass is recalculated without using the lens equation and compared to a lensing cluster.
We propose a pedestrian review of the noncommutative standard model in its present state.
There is a natural homomorphism of Lie pseudoalgebras from local vector fields to local rotations on a Riemannian manifold. We address the question whether this homomorphism is unique and give a positive answer in the perturbative regime around the flat metric.
The present status of Connes' noncommutative view at the four forces is reviewed.
We try to give a pedagogical introduction to Connes' derivation of the standard model of electro-magnetic, weak and strong forces from gravity.
The values of the Higgs mass are obtained for two possibilities of extending the standard model in a way compatible with the existence of a noncommutative structure at high energies. We assume the existence of a big desert between the low energy electroweak scale and the high energy scale $Λ= 1.1\times 10^{17}$ GeV, where noncommutative features become relevant. We conclude that it is extremely difficult to depart from the Higgs mass value $ m_H= 175.1^{+5.8}_{-9.8}$ GeV obtained from noncommutative geometry for the standard model with three generations only.
We compute the linear responses of the Hubble diagram to small scalar perturbations in the Robertson-Walker metric and to small peculiar velocities of emitter and receiver. We discuss the monotonicity constraint of the Hubble diagram in the light of these responses.
We present a lower bound on the radius of the universe today $a_0$ and a monotonicity constraint on the Hubble diagram. Our theoretical input is Einstein's kinematics and maximally symmetric universes. Present supernova data yield $a_0 > 1.2\cdot 10^{26}$ m. A first attempt to quantify the monotonicity constraint is described. We do not see any indication of non-monotonicity.
We extend a classification of irreducible, almost commutative geometries whose spectral action is dynamically non-degenerate to internal algebras that have four simple summands.
A classification of irreducible, dynamically non-degenerate, almost commutative spectral triples is refined. It is extended to include centrally extended spin lifts. Simultaneously it is reduced by imposing three constraints: (i) the condition of vanishing Yang-Mills and mixed gravitational anomalies, (ii) the condition that the fermion representation be complex under the little group, while (iii) massless fermions are to remain neutral under the little group. These constraints single out the standard model with one generation of leptons and quarks and with an arbitrary number of colours.
Connes' noncommutative approach to the standard model of electromagnetic, weak and strong forces is sketched as well as its unification with general relativity.
We classify all irreducible, almost commutative geometries whose spectral action is dynamically non-degenerate. Heavy use is made of Krajewski's diagrammatic language. The motivation for our definition of dynamical non-degeneracy stems from particle physics where the fermion masses are non-degenerate.
The aim of this contribution is to explain how Connes derives the standard model of electromagnetic, weak and strong forces from noncommutative geometry. The reader is supposed to be aware of two other derivations in fundamental physics: the derivation of the Balmer-Rydberg formula for the spectrum of the hydrogen atom from quantum mechanics and Einstein's derivation of gravity from Riemannian geometry.