Related papers: The Fuzzy Onion: A proposal
We propose a matrix model realisation of a three-dimensional quantum space. It has an onion-like structure composed of concentric fuzzy spheres of increasing radius. The angular part of the Laplace operator is inherited from that of the…
In our previous contribution, we introduced a matrix formulation of a three-dimensional quantum space named the fuzzy onion. The novel part of the construction is the radial derivative term, which has been defined to recover the correct…
The fuzzy onion model formed by connecting a set of concentric fuzzy spheres of increasing radius is motivated by studies of quantum space but can also be used to study standard physics. The main feature of the model is that functions in…
Fuzzy spaces like the fuzzy sphere or the fuzzy torus have received remarkable attention, since they appeared as objects in string theory. Although there are many higher dimensional examples, the most known and most studied fuzzy spaces are…
A fuzzy circle and a fuzzy 3-sphere are constructed as subspaces of fuzzy complex projective spaces, of complex dimension one and three, by modifying the Laplacians on the latter so as to give unwanted states large eigenvalues. This leaves…
A family of fuzzy orbifolds are generated by looking at sub-algebras of the fuzzy sphere. One of them is actually commutative and can be mapped exactly onto a lattice. The others are fuzzy approximations of S^2/Z_N where Z_N is the cyclic…
The quantum space-time and the phase space with fuzzy structure is investigated as the possible quantization formalism. In this theory the state of nonrelativistic particle corresponds to the element of fuzzy ordered set (Foset) - fuzzy…
Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…
Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in…
Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field…
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…
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 construct higher dimensional quantum Hall systems based on fuzzy spheres. It is shown that fuzzy spheres are realized as spheres in colored monopole backgrounds. The space noncommutativity is related to higher spins which is originated…
This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…
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…
We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix model deformed by terms involving fixed…
We point out that if spatial information is encoded through linear operators $X_i$, or `infinite-dimensional matrices' with an involution $X_i^*=X_i$ then these $X_i$ can only describe either continuous, discrete or certain "fuzzy"…
Given a nonempty set $X$ and a function $f:X \rightarrow X$, three fuzzy topological spaces are introduced. Some properties of these spaces and relation among them are studied and discussed.
We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a…
In the present contribution the construction of particle physics models in theories with fuzzy extra dimensions is discussed. We focus on a bottom-up approach where the structure of a higher-dimensional theory arises within ordinary…