Related papers: Geometrical quantities on a fuzzy sphere
The paper contains a proposal for an energy and time representation. We construct modes that correspond to fuzzy distributions around discrete values of energy or time. The modes form an orthogonal and complete set in the space of square…
In plane-wave matrix model, the membrane fuzzy sphere extended in the SO(3) symmetric space is allowed to have periodic motion on a sub-plane in the SO(6) symmetric space. We consider a background configuration composed of two such fuzzy…
Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set of spherically symmetric densities determines uniquely the external potential in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations are…
Quantum Space-Time and Phase Space with fuzzy geometric structure are studied as possible formalism for quantization of massive particles and fields. In this approach the state of nonrelativistic particle m described by the fuzzy point of…
The so-called spectral dimension is a scale-dependent number associated with both geometries and field theories that has recently attracted much attention, driven largely though not exclusively by investigations of causal dynamical…
This is a short review of recent work on fuzzy spaces in their relation to the M(atrix) theory and the quantum Hall effect. We give an introduction to fuzzy spaces and how the limit of large matrices is obtained. The complex projective…
In this work, topological spaces are enriched by additional structures in order to give a more realistic representation of real life phenomena and computational processes and at the same time, to provide for utilization of the powerful…
We consider the energy functional on the space of sections of a sphere bundle over a Riemannian manifold (M, <,>) equipped with the Sasaki metric and we discuss the characterising condition for critical points. Likewise, we provide a useful…
We review the description of scalar field theories on fuzzy spaces by Hermitian random matrix models. After reminding the reader of the relevant aspects of the random matrix theory and construction of the fuzzy spaces, we summarize the most…
Modification of nonrelativistic phase space structure based on fuzzy ordered sets (Fosets) structure investigated as a possible quantization framework. In this model particle's $m$ state corresponds to Foset element - fuzzy point. Due to…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
The null-surface formulation of general relativity -- recently introduced -- provides novel tools for describing the gravitational field, as well as a fresh physical way of viewing it. The new formulation provides ``local'' observables…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
Electromagnetic quantities such as energy density, momentum, spin, and helicity bring meaning and intuition to electromagnetism and possess intricate interrelations, particularly prominent in complex non-paraxial near-fields. These…
Functionals involving surface curvature are important across a range of scientific disciplines, and their extrema are representative of physically meaningful objects such as atomic lattices and biomembranes. Inspired in particular by the…
The quasiradial wave functions and energy spectra of the alternative model of spherical oscillator on the $D$-dimensional sphere and two-sheeted hyperboloid are found.
The goal of this work is to introduce and study fuzzy limits of functions. Two approaches to fuzzy limits of a function are considered. One is based on the concept of a fuzzy limit of a sequence, while another generalizes the conventional…
We begin by studying the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of the semi-axes. We write down an explicit formula as an integral over the unit sphere in n-dimensions and use this…
The proper resolution of the so-called measurement problem requires a "top-down" conception of the quantum world that is opposed to the usual "bottom-up" conception, which builds on an intrinsically and maximally differentiated manifold.…
The letter provides a geometrical interpretation of frequency in electric circuits. According to this interpretation, the frequency is defined as a multivector with symmetric and antisymmetric components. The conventional definition of…