Related papers: On Marshak's and Connes' views of chirality
The decomposition of the non-commutative Landau (NCL) system into two uncoupled one-dimensional chiral components, advocated by Alvarez, Gomis, Kamimura and Plyushchay [1], is generalized to nonvanishing electric fields. This allows us to…
We discuss that the Ginsparg-Wilson relation, which has the key role in the recent development of constructing lattice chiral gauge theory, can play an important role to define chiral structures in finite matrix models and noncommutative…
We develop an alternative formulation of the symmetry breaking sector of the Standard Model as a gauged non-linear sigma model (NLSM) following the philosophy of the Chiral lagrangian approach, which is the only compatible with all the…
A survey of the interrelationships between matrix models and field theories on the noncommutative torus is presented. The discretization of noncommutative gauge theory by twisted reduced models is described along with a rigorous definition…
This is a short review of the relation between the Reduced Models and Noncommutative Yang-Mills Theories (NCYM) based on the work done in collaboration with J. Ambjorn, J. Nishimura and R. Szabo. Contents: 1.Twisted Eguchi-Kawai model…
Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation…
We render a thorough, physicist's account of the formulation of the Standard Model (SM) of particle physics within the framework of noncommutative differential geometry (NCG). We work in Minkowski spacetime rather than in Euclidean space.…
Connes' noncommutative approach to the standard model of electromagnetic, weak and strong forces is sketched as well as its unification with general relativity.
An extension of the Connes--Lott model is proposed. It is also within the framework of the A.Connes construction based on a generalized Dirac--Yukawa operator and the K--cycle $(H,D)$, with $H$ a fermionic Hilbert space. The basic algebra…
This informal introduction is an extended version of a three hours lecture given at the 6th Peyresq meeting ``Integrable systems and quantum field theory''. In this lecture, we make an overview of some of the mathematical results which…
Connes' notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterepretation of the standard model of particle physics, coupled to Einstein gravity. We suggest a simple reformulation with two key…
Algebraic Yang-Mills-Higgs theories based on noncommutative geometry have brought forth novel extensions of gauge theories with interesting applications to phenomenology. We sketch the model of Connes and Lott, as well as variants of it,…
After some recalls on the standard (non)-linear $\sigma$ model, we discuss the interest of B.R.S. symmetry in non-linear $\sigma$ models renormalisation. We also emphasise the importance of a correct definition of a theory through physical…
A very specific two-Higgs-doublet extension of the Glashow-Salam-Weinberg model for one generation of quarks is advocated for, in which the two doublets are parity transformed of each other and both isomorphic to the Higgs doublet of the…
In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The…
This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant $K$-theory of the cotangent bundle of the…
By introducing a notion of smooth connection for unbounded $KK$-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of…
We give an introduction to the recently established connection between supersymmetric gauge theories and matrix models. We begin by reviewing previous material that is required in order to follow the latest developments. This includes the…
We compute the magnetic susceptibility of the quark condensate and the polarization of quarks at zero temperature and in a uniform magnetic background. Our theoretical framework consists of two chiral models that allow to treat…
We establish the existence of one-loop finite relations between the Cabibbo angle and the quark mass ratios, in the Standard Model with one Higgs doublet and two quark generations. Assuming a simple quark-lepton universality, we use the…