Related papers: The Fuzzy S^4 by Quantum Deformation
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
We introduce the Quantum Holonomy-Diffeomorphism *-algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical…
Various applications of quantum algebraic techniques in nuclear structure physics, such as the su$_q$(2) rotator model and its extensions, the use of deformed bosons in the description of pairing correlations, and the construction of…
A global model of $q$-deformation for the quasi--orthogonal Lie algebras generating the groups of motions of the four--dimensional affine Cayley--Klein geometries is obtained starting from the three dimensional deformations. It is shown how…
We summarize our recent construction of new fuzzy hyperspheres $S^d_{\Lambda}$ of arbitrary dimension $d$ covariant under the {\it full} orthogonal group $O(D)$, $D=d+1$. We impose a suitable energy cutoff on a quantum particle in…
In this paper, we explore the quantization of K\"ahler manifolds, focusing on the relationship between deformation quantization and geometric quantization. We provide a classification of degree 1 formal quantizable functions in the…
A construction of the 2d and 4d fuzzy de Sitter hyperboloids is carried out by using a (vector) coherent state quantization. We get a natural discretization of the dS "time" axis based on the spectrum of Casimir operators of the respective…
We argue supersymmetric generalizations of fuzzy two- and four-spheres based on the unitary-orthosymplectic algebras, $uosp(N|2)$ and $uosp(N|4)$, respectively. Supersymmetric version of Schwinger construction is applied to derive graded…
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which…
We give a simple geometric description of all formal deformation quantizations on a K\"ahler manifold $M$ which enjoy the following property of separation of variables into holomorphic and antiholomorphic ones. For each open subset…
We define a class of $A_\infty$-algebras that are obtained by deformations of higher spin symmetries. While higher spin symmetries of a free CFT form an associative algebra, the slightly broken higher spin symmetries give rise to a minimal…
We formulate a model of noncommutative four-dimensional gravity on a covariant fuzzy space based on SO(1,4), that is the fuzzy version of the $\text{dS}_4$. The latter requires the employment of a wider symmetry group, the SO(1,5), for…
Using $\star$-product on Co-adjoint orbits (K-orbits) of the $\MD_4$- groups we obtain quantum half-planes, quantum hyperbolic cylinders, quantum hyperbolic paraboloids...via Fedosov deformation quantization. From this we have corresponding…
We study the quantization of compact space on the basis of the Moyal quantization. We first construct the $su(2)$ algebra that are the functions of canonical coordinates $a$ and $a^*$. We make use of them to define the adjoint operators,…
We recall a construction of non-commutative algebras related to a one-parameter family of (deformed) spheres and tori, and show that in the case of tori, the *-algebras can be completed into C*-algebras isomorphic to the standard…
We examine in detail the higher spin fields which arise on the basic fuzzy sphere $S^4_N$ in the semi-classical limit. The space of functions can be identified with functions on classical $S^4$ taking values in a higher spin algebra…
Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are…
We introduce non-commutative algebras, which can be associated with the function algebra of functions on a finite or half-finite cylinder. The algebras, which depend on a deformation parameter, are crossed product algebras of a partial…
In 2006 we proposed Quantum Fuzzy Sets, observing that states of a quantum register could serve as characteristic functions of fuzzy subsets, embedding Zadeh's unit interval into the Bloch sphere. That paper was deliberately preliminary. In…
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the…