Related papers: Fuzzy Torus and q-Deformed Lie Algebra
Our aim in this thesis is to use the language of deformation-quantization to understand certain quantized algebras by looking at properties of the corresponding commutative ones, and conversely to obtain results about the commutative…
We study in one-loop perturbation theory noncommutative fuzzy quenched QED_4. We write down the effective action on fuzzy S**2 x S**2 and show the existence of a gauge-invariant UV-IR mixing in the model in the large N planar limit. We also…
A 3-parametric two-sided deformation of Heisenberg algebra (HA), with p,q-deformed commutator in the l.h.s. of basic defining relation and certain deformation of its r.h.s., is introduced and studied. The third deformation parameter \mu…
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.…
A two-parameter deformed superoscillator system with SUq1/q2(n|m)-covariance is presented and used to construct a two-parameter deformed N=2 SUSY algebra. The Fock space representation of the algebra is discussed and the deformed…
The deformed $W$-algebra is a quantum deformation of the $W$-algebra ${\cal W}_\beta(\mathfrak{g})$ in conformal field theory. Using the free field construction, we obtain a closed set of quadratic relations of the $W$-currents of the…
An extra term generally appears in the q-deformed $su(2)$ algebra for the deformation parameter $q = \exp{ 2 \pi i\theta}$, if one combines the Biedenharn-Macfarlane construction of q-deformed $su(2)$, which is a generalization of…
New results are added to the paper [4] about q-closed and solvable sesquilinear forms. The structure of the Banach space $\mathcal{D}[||\cdot||_\Omega]$ defined on the domain $\mathcal{D}$ of a q-closed sesquilinear form $\Omega$ is unique…
An algebra homomorphism $\psi$ from the q-deformed algebra $U_q({\rm iso}_2)$ with generating elements $I$, $T_1$, $T_2$ and defining relations $[I,T_2]_q=T_1$, $[T_1,I]_q=T_2$, $[T_2,T_1]_q=0$ (where $[A,B]_q=q^{1/2}AB-q^{-1/2}BA$) to the…
In this paper, we propose a full characterization of a generalized $q-$deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the…
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…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to…
We study the one loop dynamics of QFT on the fuzzy sphere and calculate the planar and nonplanar contributions to the two point function at one loop. We show that there is no UV/IR mixing on the fuzzy sphere. The fuzzy sphere is…
We consider $\rm R$-matrix realization of the quantum deformations of the loop algebras $\tilde{\mathfrak{g}}$ corresponding to non-exceptional affine Lie algebras of type $\hat{\mathfrak{g}}=A^{(1)}_{N-1}$, $B^{(1)}_n$, $C^{(1)}_n$,…
In this paper, we follow a Bootstrap-like approach to determine the most restricted form the finiteness constraint $\mathcal{F}(q,g,h,\kappa)$, which relates the four parameters of $\mathcal{N}=1$ Leigh-Strassler (LS) deformed models, by…
We study chiral deformations of ${\cal N}=2$ and ${\cal N}=4$ supersymmetric gauge theories obtained by turning on $\tau_J \,{\rm tr} \, \Phi^J$ interactions with $\Phi$ the ${\cal N}=2$ superfield. Using localization, we compute the…
We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…
I introduce a reality structure on the Heisenberg double of Fun_q(SL(N,C)) for q phase, which for N=2 can be interpreted as the quantum phase space of the particle on the q-deformed mass-hyperboloid. This construction is closely related to…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…