Related papers: The Garden of Quantum Spheres
Even though it has been almost a century since quantum mechanics planted roots, the field has its share of unresolved problems. It could be the result of a wrong mathematical structure providing inadequate understanding of the quantum…
Spherical field theory is a new non-perturbative method for studying quantum field theories. It uses the spherical partial wave expansion to reduce a general d-dimensional Euclidean field theory into a set of coupled one-dimensional…
We review various aspects of (infinite) quantum group symmetries in 2D massive quantum field theories. We discuss how these symmetries can be used to exactly solve the integrable models. A possible way for generalizing to three dimensions…
The quantum deformation $CP_q(N)$ of complex projective space is discussed. Many of the features present in the case of the quantum sphere can be extended. The differential and integral calculus is studied and $CP_q(N)$ appears as a quantum…
In this paper, on envelopes created by sphere families in Euclidean 3-space, all four basic problems (existence problem, representation problem, problem on the number of envelopes, problem on relationships of definitions) are solved.
In this paper, we have firstly presented a new quantum theory to study one-dimensional photonic crystals. We give the quantum transform matrix, quantum dispersion relation and quantum transmissivity, and compare them with the classical…
The article demonstrates the nontrivial manifestation of quantum shell effects in a compressed mesoscopic system. It is shown that there are two spatial scales in the distribution of degenerate electrons in a spherical well. The first scale…
For $\mu \in (0,1), c> 0,$ we identify the quantum group $SO_\mu(3)$ as the universal object in the category of compact quantum groups acting by `orientation and volume preserving isometries' in the sense of \cite{goswami2} on the natural…
In this paper, we consider the geometrical quantities on the fuzzy sphere from the spectral point of view, such as the area and the dimension. We find that, in contract to the standard sphere, the area and the dimension are the functions of…
We will show that for any $n\ge N$ points on the $N$-dimensional sphere $S^N$ there is a closed hemisphere which contains at least $\lfloor\frac{n+N+1}{2}\rfloor$ of these points. This bound is sharp and we will calculate the amount of sets…
Presently about 3000 different nuclei are known with about another 3000-4000 predicted to exist. A review of the discovery of the nuclei, the present status and the possibilities for future discoveries are presented.
Short review of riddles that lie at the intersection of quantum theory, particle physics and cosmology; dark energy as false vacuum; discussion of a possible detection experiment.
This is an introductory set of lecture notes on quantum cosmology, given in 1995 to an audience with interests ranging from astronomy to particle physics. Topics covered: 1. Introduction: 1.1 Quantum cosmology and quantum gravity; 1.2 A…
Quantum field theory at finite temperature and density can be used for describing the physics of relativistic plasmas. Such systems are frequently encountered in astrophysical situations, such as the early Universe, Supernova explosions,…
Three classes of finite-dimensional models of quantum systems exhibiting spectral degeneracies called quantum catastrophes are described in detail. Computer-assisted symbolic manipulation techniques are shown unexpectedly efficient for the…
The quantum flag manifold ${SU_q(3)/\mathbb{T}^2}$ is interpreted as a noncommutative bundle over the quantum complex projective plane with the quantum or Podle\'s sphere as a fibre. A connection arising from the (associated) quantum…
We concern with various aspects of equilibrium and non-equilibrium quantum field theory.
Using virtual spin formalism it is shown that a quantum particle with eight energy levels can store three qubits. The formalism allows to realize a universal set of quantum gates. Feasible formalism implementation is suggested which uses…
This is a survey paper of the theory of crystal bases, global bases and the cluster algebra structure on the quantum coordinate rings.
Any four mutually tangent spheres in R^3 determine three coincident lines through opposite pairs of tangencies. As a consequence, we define two new triangle centers.