Related papers: Geometrical quantities on a fuzzy sphere
I describe and analyze the various energy scales that emerge from studying the structure of the Standard Models of particle physics and cosmology. Remarkably, save for the scale of the cosmological vacuum energy, all the scales below the…
The `Chern-Simons Quantum Mechanics' of a particle on CP(n|m) is shown to yield the fuzzy descriptions of these superspaces, for which we construct the non-(anti)commuting position operators. For a particle on the supersphere CP(1|1) =…
This paper provides an overview on tools from potential theory on the sphere and some applications in geoscience.
The model of a scalar field with quartic self-interaction on the fuzzy sphere has three known phases: a uniformly ordered phase, a disordered phase and a non-uniformly ordered phase, the last of which has no classical counterpart. These…
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…
We investigate the properties of $Q$-balls in $d$ spatial dimensions. First, a generalized virial relation for these objects is obtained. We then focus on potentials $V(\phi\phi^{\dagger})= \sum_{n=1}^{3} a_n(\phi\phi^{\dagger})^n$, where…
I discuss a scaling limit, where open strings in the WZW-model behave as dipoles with charges confined to a spherical brane and projected to the lowest Landau level. Then I show how the joining and splitting interactions of these dipoles…
The effect of the curvature of a cylindrical surface on the energy spectrum for a curved two-dimensional electron gas in a homogeneous magnetic field is considered. The corrections to the energy spectrum are obtained for the first time…
The critical properties of the real phi^4 scalar field theory are studied numerically on the fuzzy sphere. The fuzzy sphere is a matrix (non commutative) discretisation of the algebra of functions on the usual two dimensional sphere. It is…
The concepts of fuzzy objects and their classes are described that make it possible to structurally represent knowledge about fuzzy and partially-defined objects and their classes. Operations over such objects and classes are also proposed…
This work provides a necessary and sufficient condition for the isomorphism of two fuzzy subspaces in terms of their dimensions.
We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to…
The two dimensional surface of a sphere can be parametrized by coordinates representing two charged pions acting as Goldstone bosons of a broken $SU_2$ symmetry. We construct in full concrete detail, and in a general class of coordinate…
We derive a simple rule to determine surface plasmon energies, based on the geometrical properties of the surface of the metal. We apply this concept to obtain the surface plasmon energies in wedges, corners and conical tips. The results…
The vacuum energy of a conformally coupled scalar field on the d-dimensional sphere is calculated. On even spheres it is zero and on odd spheres it oscillates in sign. Results for the d-torus and d-cube are also given.
Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions…
Monopoles and solitons have important topological aspects like quantized fluxes, winding numbers and curved target spaces. Naive discretizations which substitute a lattice of points for the underlying manifolds are incapable of retaining…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
We discuss a two-body interaction of membrane fuzzy spheres in a pp-wave matrix model at finite temperature by considering a fuzzy sphere rotates with a constant radius r around the other one sitting at the origin in the SO(6) symmetric…