Related papers: Noncommutative Geometry and Particle Physics
By exploring possible physical sense of notions, structures, and logic in a class of noncommutative geometries, we try to unify the four fundamental interactions within an axiomatic quantum picture. We identify the objects and algebraic…
Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum…
The standard model taken with a momentum space cut-off may be viewed as an effective low energy theory. The structure of it and its known parameters can give us hints for relations between these parameters. In the present investigation the…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality…
We derive Bogomolny-type equations for the Abelian Higgs model defined on the noncommutative torus and discuss its vortex like solutions. To this end, we carefully analyze how periodic boundary conditions have to be handled in…
Extensions of the Standard Model of elementary particle physics to noncommutative geometries are proposed by string models. Independent of this motivation, one may consider such a model as an effective field theory with higher-dimensional…
It is pointed out (not for the first time) that the minimal Standard Model, without additional gauge-singlet right-handed neutrinos or isotriplet Higgs fields, allows for nonvanishing neutrino masses and mixing. The required interaction…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
We consider a complex singlet scalar in the spectral action approach to the standard model. It is shown that there is a range of initial values at the unification scale which is able to produce Higgs and top quark masses at low energies.…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces…
This is a survey of the historical development of the Spectral Standard Model and beyond, starting with the ground breaking paper of Alain Connes in 1988 where he observed that there is a link between Higgs fields and finite noncommutative…
Cosmological consequences of the noncommutative geometry spectral action are presented. Neglecting the nonminimal coupling of the Higgs field to the curvature, background cosmology remains unchanged, and only the inhomogeneous perturbations…
On basis of an algebraic analysis of symmetry breaking in general and the Higgs mechanism in the standard model of elementary particles we generalize the concept of symmetry breaking to systems with non-compact groups but not necessarily…
We propose a new action principle to be associated with a noncommutative space $(\Ac ,\Hc ,D)$. The universal formula for the spectral action is $(\psi ,D\psi) + \Trace (\chi (D /$ $\Lb))$ where $\psi$ is a spinor on the Hilbert space,…
We consider astrophysical objects such as main-sequence stars, white-dwarfs and neutron stars in a noncommutative context. Noncommutativity is implemented via a deformed dispersion relation $E^{2}=p^{2}c^{2}(1+\lambda E)^{2}+m^{2}c^{4}$…
We present a combinatorial problem which consists in finding irreducible Krajewski diagrams from finite geometries. This problem boils down to placing arrows into a quadratic array with some additional constrains. The Krajewski diagrams…
We introduce the standard model of elementary particles and discuss the reasons why we have to modify it. Emphasis is put on the indications from the neutrinos and on the role of the Higgs particle; some promising theoretical ideas, like…