相关论文: Notes on Connes' Construction of the Standard Mode…
Massive neutrinos can be accommodated into the noncommutative geometry reinterpretation of the Standard Model. The constrained Standard Model Lagrangian is computed anew under the assumption of nonzero neutrino masses. This gives the…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex…
Gauge unification is widely considered to be a desirable feature for extensions of the standard model. Unfortunately the standard model itself does not exhibit a unification of its running gauge couplings but it is required by grand unified…
We present a physical interpretation of the doubling of the algebra, which is the basic ingredient of the noncommutative spectral geometry, developed by Connes and collaborators as an approach to unification. We discuss its connection to…
A natural extension of the standard model within non-commutative geometry is presented. The geometry determines its Higgs sector. This determination is fuzzy, but precise enough to be incompatible with experiment.
The structure of the standard model is concisely summarized, including the standard model Lagrangian, spontaneous symmetry breaking, the reexpression of the Lagrangian in terms of mass eigenstates after symmetry breaking, and the gauge…
Using the notion of a gauge connection on a flat superspace, we construct a general class of noncommutative ($D=2,$ $\mathcal{N}=1$) supertranslation algebras generalizing the ordinary algebra by inclusion of some new bosonic and fermionic…
Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the…
The unimodularity condition in Connes' formulation of the standard model is rewritten in terms of group representations.
The successes and shortcomings of the Standard Model are reviewed, with emphasis on the reasons motivating the need to extend it. The basic elements of grand unification and supersymmetry are described, exploring their phenomenological…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
It is well known that anomaly cancellation {\it almost} determines the hypercharges in the standard model. A related (and somewhat more stronger) phenomenon takes place in Connes' NCG framework: unimodularity (a technical condition on…
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…
We review the construction of particle physics models in the framework of non-commutative geometry. We first give simple examples, and then progress to outline the Connes-Lott construction of the standard Weinberg-Salam model and our…
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to…
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played…
The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the…
We propose a new point of view to gauge theories based on taking the action of symmetry transformations directly on the coordinates of space. Via this approach the gauge fields are not introduced at the first step, and they can be…
Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the…