Related papers: A spectral geometry for the Standard Model without…
We re-examine the non Hermitian position coordinate of Dirac's equation, in the light of his own insights and conclude that this, and the Dirac equation itself is symptomatic of an underlying Noncommutative Geometry.
We review a possible solution to the fermion generation puzzle based on a nonabelian generalization of electric--magnetic duality derived some years ago. This nonabelian duality implies the existence of another SU(3) symmetry dual to…
We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of…
A model of an extended manifold for the Dirac spinor field is considered. Two Lagrangians related by CPTM (charge-parity-time-mass) symmetry are constructed for a pair of the Dirac spinor fields with each spinor field defined in a separate…
The twined almost commutative structure of the standard spectral triple on the noncommutative torus with rational parameter is exhibited, by showing isomorphisms with a spectral triple on the algebra of sections of certain bundle of…
The Standard Model (SM) of particle physics is in such good agreement with experiment that it is still accepted as providing an accurate model of reality. Nevertheless, its algebraic foundations are in need of repair. Chirality is shown to…
Extensions of the Standard Model of elementary particle physics to noncommutative geometries have been proposed as a low energy limit of string models. Independent of this motivation, one may consider such a model as an effective field…
The Conformal Standard Model (CSM) is a minimal extension of the Standard Model of Particle Physics based on the assumed absence of large intermediate scales between the TeV scale and the Planck scale, which incorporates only right-chiral…
We consider the scattering of quasi-particles off the boundary created during a first order electroweak phase transition. Spatial coherence is lost due to the quasi-quark damping rate, and we show that reflection on the boundary is…
The special features of CP violation in the Standard Model are presented. The significance of measuring CP violation in B, K and D decays is explained. The predictions of the Standard Model for CP asymmetries in B decays are analyzed in…
We argue that some features of the standard model, in particular the fermion assignment and symmetry breaking, can be obtained in matrix model which describes noncommutative gauge theory as well as gravity in an emergent way. The mechanism…
Study of the Weyl and Dirac topological materials (topological semimetals, insulators, superfluids and superconductors) opens the route for the investigation of the topological quantum vacua of relativistic fields. The symmetric phase of…
We discuss some properties of the spectral triple $(A_F,H_F,D_F,J_F,\gamma_F)$ describing the internal space in the noncommutative geometry approach to the Standard Model, with $A_F=\mathbb{C}\oplus\mathbb{H}\oplus M_3(\mathbb{C})$. We show…
We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.
A non-zero CP-violating $\theta$ parameter is treated in the domain model which assumes a cluster-like vacuum structure whose units are characterised in particular by a topological charge which is not necessarily an integer number. In the…
We investigate the representation of diffeomorphisms in Connes' Spectral Triples formalism. By encoding the metric and spin structure in a moving frame, it is shown on the paradigmatic example of spin semi-Riemannian manifolds that the…
We address in this work the question of the discretization of two-dimensional periodic Dirac Hamiltonians. Standard finite differences methods on rectangular grids are plagued with the so-called Fermion doubling problem, which creates…
We investigate the interplay between confinement and the fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. First, simple electrostatic gates do not confine electrons due to the Klein tunneling.…
The effect of disorder on the Landau levels of massless Dirac fermions is examined for the cases with and without the fermion doubling. To tune the doubling a tight-binding model having a complex transfer integral is adopted to shift the…
Simply on CP arguments, we argue against a Standard Model explanation of baryogenesis via the charge transport mechanism. A CP-asymmetry is found in the reflection coefficients of quarks hitting the electroweak phase boundary created during…