Related papers: Noncommutative geometry of the quantum clock
The phenomenological investigation of noncommutative space-time in the laboratory frame are presented. We formulate the apparent time variation of noncommutativity parameter $\theta_{\mu\nu}$ in the laboratory frame due to the earth's…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
In this talk, we review the basics concepts of fuzzy physics and quantum field theory on the Groenwald-Moyal Plane as examples of noncommutative spaces in physics. We introduce the basic ideas, and discuss some important results in these…
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…
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.…
Recently Verlinde proposed that gravity can be described as an emergent phenomena arising from changes in the information associated with the positions of material bodies. By using noncommutative geometry as a way to describe the…
Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism…
Effects of noncommutativity are investigated in planar quantum mechanics in the coordinate representation. Generally these issues are addressed by converting to the momentum space. In the first part of the work we show noncommutative…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
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…
Non Commutative Geometry (NCG) is considered in the context of a charged particle moving in a uniform magnetic field. The classical and quantum mechanical treatments are revisited and a new marker of NCG is introduced. This marker is then…
To explore the properties of space and initial singularities in the context of general relativity, where spacetime becomes poorly defined and no longer belongs to a regular manifold, we examine the evolution of the expansion of timelike…
We present a short review describing the use of noncommutative space-time in quantum-deformed dynamical theories: classical and quantum mechanics as well as classical and quantum field theory. We expose the role of Hopf algebras and their…
We investigate the effect of the noncommutative geometry on the classical orbits of particles in a central force potential. The relation is implemented through the modified commutation relations $[x_i, x_j]=i \theta_{ij} $. Comparison with…
We review a gravitational model based on noncommutative geometry and the spectral action principle. The space-time geometry is described by the tensor product of a four-dimensional Riemanian manifold by a discrete noncommutative space…
A model unifying general relativity with quantum mechanics is further developed. It is based on a noncommutative geometry which supposedly modelled the universe in its pre-Planckian epoch. The geometry is totally nonlocal with no time and…
We examine the geometry of a generalized uncertainty-inspired quantum black hole. The diagonal line element is not $t$-$r$ symmetric, i.e. $g_{00} \ne -1/g_{11}$, which leads to an interesting approach to resolving the classical curvature…
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…
A deformed relativistic kinematics can be understood within a geometrical framework through a maximally symmetric momentum space. However, when considering this kind of approach, usually one works in a flat spacetime and in a curved…
These lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate…