Related papers: Particle and Field Symmetries and Noncommutative G…
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…
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…
Application of the noncommutative geometry to several physical models is considered.
Analysis of the covariant theta-exact noncommutative (NC) gauge field theory (GFT), inspired by high energy cosmic rays experiments, is performed in the framework of the inelastic neutrino-nucleon scatterings. Next we have have found…
I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the…
Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…
The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures --such as triad and area operators-- exhibit a non-commutativity. At first…
We introduce topological gauge fields as nontrivial field configurations enforced by topological currents. These fields crucially determine the form of statistical gauge fields that couple to matter and transmute their statistics. We…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.
This report provides a brief review of recently developed extended framework for fundamental physics, designated as Quantum Field Mechanics and including causally complete and intrinsically unified theory of explicitly emerging elementary…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
Here we present an overview on the various works, in which many collaborators have contributed, regarding the interesting dipole of noncommutativity and physics. In brief, we present the features that noncommutativity triggers both in the…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
There are two very important subjects in physics: Symmetry of dynamical models and nonlinearity. All really fundamental models are invariant under some particular symmetry groups. There is also no true physics, no our Universe and life at…