Related papers: Noncommutative Gravity and the Standard-Model Exte…
After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois…
The progress of noncommutative geometry has been crucially influenced, from the beginning, by quantum physics: we review this development in recent years. The Standard Model, with its central role for the Dirac operator, led to several…
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…
This thesis explores the cosmological implications of modified gravity, focusing on nonmetricity-based $f(Q)$ gravity as an alternative to the $\Lambda$CDM model in explaining cosmic acceleration. Chapter I lays the theoretical groundwork…
We study $\gamma\gamma$ scattering in noncommutative QED (NCQED) where the gauge field has Yang-Mills type coupling, giving new contributions to the scattering process and making it possible for it to occur at tree level. The process takes…
We study all possible $U(1)$-extensions of the standard model (SM) in the framework of noncommutative geometry (NCG) with the algebra $\hhh\op\cc\op\cc\op M_3(\cc)$. Comparison to experimental data about the mass of a hypothetical $Z'$…
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
Non-invertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible…
In this paper we investigate a model for quantum gravity on finite noncommutative spaces using the theory of blobbed topological recursion. The model is based on a particular class of random finite real spectral triples ${(\mathcal{A},…
Our aim in this review article is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the…
We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in the framework of compact quantum group theory and…
The Standard-Model Extension (SME) is the general phenomenological framework used to investigate Lorentz violation at the level of effective field theory. It has been used to obtain stringent experimental bounds on Lorentz violation in a…
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 this paper I discuss connections between the noncommutative geometry approach to the standard model on one side, and the internal space coming from strings on the other. The standard model in noncommutative geometry is described via the…
In this short article accessible for non-experts I discuss possible ways of constructing a non-commutative gravity paying special attention to possibilities of realizing the full diffeomorphism symmetry and to relations with 2D gravities.
A modification of General Relativity that is based on the gravitational Standard-Model Extension and incorporates nondynamical background fields has recently been studied via the ADM formalism. Our objective in this paper is to develop a…
We give a brief non-technical introduction to non-regular spacetime geometry. In particular, we discuss how curvature, and hence gravity, can be defined without a smooth (differential geometric) calculus.
We consider noncommutative geometries obtained from a triangular Drinfeld twist and review the formulation of noncommutative gravity. A detailed study of the abelian twist geometry is presented, including the fundamental theorem of…
We briefly discuss some possible cosmological implications of noncommutative geometry. While the noncommutativity we consider does not affect gravity, it can play an important role in the dynamics of other fields that are present in the…