Related papers: Noncommutative Geometry and the Standard Model: An…
A notion of fundamental group of spectral triples has been introduced. The notion uses a noncommutative analogue of unramified coverings. It was shown that in commutative case this fundamental group is a profinite completion of fundamental…
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
A reinterpretation of noncommutativity as a mapping of paths is proposed at the level of quantum mechanics.
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…
These notes are an expanded version of the author's lectures at the graduate workshop "Noncommutative Algebraic Geometry" at the Mathematical Sciences Research Institute in June 2012. The main topics discussed are Artin-Schelter regular…
We have a well-established standard model for cosmology and prospects for considerable additions from work in progress. I offer a list of elements of the standard model, comments on controversies in the interpretation of the evidence in…
Particle physics has evolved a coherent model that characterizes forces and particles at the most elementary level. This Standard Model, built from many theoretical and experimental studies, is in excellent accord with almost all current…
We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the…
We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182.
A minimal supersymmetric standard model on noncommutative space-time (NC MSSM) is proposed. The model fulfils the requirements of noncommutative gauge invariance and absence of anomaly. The existence of supersymmetry with a scale of its…
This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with…
MSc thesis of the author offering an introduction to the operator algebraic approach to noncommutative geometry, with a treatment of some more advanced elements such as the noncommutative geometry of quantum groups, fuzzy physics, and…
The known fundamental symmetries and interactions are well described by the Standard Model. Features of this powerful theory, which are described but not deeper explained, are addressed in a variety of speculative models. Experimental tests…
In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have proposed a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry was developed in terms of a noncommutative algebra…
Quantum field theory currently has a single standard mathematical characterization (the Standard Model), but no single accepted conceptual framework to interpret the mathematics. Many of these conceptualizations rely on intuitive concepts…
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…
The standard model of particle physics represents the cornerstone of our understanding of the microscopic world. In these lectures we review its contents and structure, with a particular emphasis on the central role played by symmetries and…
Using renormalization group techniques, we examine several interesting relations among masses and mixing angles of quarks and leptons in the Standard Model. We extend the analysis to the minimal supersymmetric extension to determine its…
We describe some recent progress in our understanding of Yang-Mills theories formulated on noncommutative spaces and in particular how to formulate the standard model on such spaces.