Related papers: Can (noncommutative) geometry accommodate leptoqua…
We analyse the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry.…
We discuss an extension of the standard model (SM) with vector and scalar leptoquarks. The renormalizable leptoquark Lagrangian consistent with the SM gauge symmetry is presented including the leptoquark-Higgs interactions previously not…
This talk is an introduction to ideas of non-commutative geometry and star products. We will discuss consequences for physics in two different settings: quantum field theories and astrophysics. In case of quantum field theory, we will…
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
Precision measurements of branching fractions and CP asymmetries in non-leptonic b -> s decays reveal certain "puzzles" when compared with Standard Model expectations based on a global fit of the CKM triangle and general theoretical…
New developments on the symmetries of non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a…
A brief introduction to the Standard-Model Extension (SME) approach to testing CPT and Lorentz symmetry is provided. Recent proposals for tests with antimatter are summarized, including gravitational and spectroscopic tests.
We propose and discuss how basic notions (quadratic modules, positive elements, semialgebraic sets, Archimedean orderings) and results (Positivstellensaetze) from real algebraic geometry can be generalized to noncommutative $*$-algebras. A…
We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under…
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic…
In recent years, several quantizations of real manifolds have been studied, in particular from the point of view of Connes' noncommutative geometry. Less is known for complex noncommutative spaces. In this paper, we review some recent…
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…
The mathematical apparatus of non commutative geometry and operator algebras which Connes has brought to bear to construct a rational scheme for the internal symmetries of the standard model is presented from the physicist's point of view.…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain…
We study a gauge $B-L$ extension of the standard model of quarks and leptons with unconventional charges for the singlet right-handed neutrinos, and extra singlet scalars, such that a residual $Z_3$ symmetry remains after the spontaneous…
We consider aspects of the noncommutative approach to the standard model based on the spectral action principle. We show that as a consequence of the incorporation of the Clifford structures in the formalism, the spectral action contains an…
We construct F-theory GUT models without exotic matter, leading to the MSSM matter spectrum with potential singlet extensions. The interplay of engineering explicit geometric setups, absence of four-dimensional anomalies, and realistic…
Recently, a correspondence has been shown to exist between the structure of a single Standard Model generation of elementary particles and the properties of the Clifford algebra of nonrelativistic phase space. Here, this correspondence is…
The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a…