Related papers: Two Non--Commutative U(1)-Gauge Laplacians in the …
Quantum planes which correspond to all one parameter solutions of QYBE for the two-dimensional case of GL-groups are summarized and their geometrical interpretations are given. It is shown that the quantum dual plane is associated with an…
We discuss the quantum mechanics of a particle in a magnetic field when its position x^{\mu} is restricted to a periodic lattice, while its momentum p^{\mu} is restricted to a periodic dual lattice. Through these considerations we define…
The leitmotiv of this review is noncommutative principal U(1)-bundles and associated line bundles. In the first part I give a brief introduction to Hopf-Galois theory and its applications, from field extensions to principal group actions. I…
The light-cone Hamiltonian approach is applied to the super D2-brane, and the equivalent area--preserving and U(1) gauge-invariant effective Lagrangian, which is quadratic in the U(1) gauge field, is derived. The latter is recognised to be…
We consider Laplace operators on periodic discrete graphs perturbed by guides, i.e., graphs which are periodic in some directions and finite in other ones. The spectrum of the Laplacian on the unperturbed graph is a union of a finite number…
We consider Laplacians with non unitary twists acting on sections of flat vector bundles over compact hyperbolic surfaces. These non self-adjoint Laplacians have discrete spectrum inside a parabola in the complex plane. For representations…
Let $G$ be a Lie group, $\g$ its Lie algebra, and $U_h(\g)$ the corresponding quantum group. We consider some examples of $U_h(\g)$-invariant one and two parameter quantizations on $G$-manifolds.
The heavy quarkonium spectrum of Two Color QCD (QC$_2$D) at non-zero quark chemical potential $\mu$ and temperature $T$ with $\mu/T\gg1$ has been calculated in both $S$- and $P$-wave channels using a lattice non-relativistic formulation of…
The two-parametric quantum deformation of the algebra of coordinate functions on the supergroup GL$(1| 1)$ via a contraction of GL$_{p,q}(1| 1)$ is presented. Related differential calculus on the quantum superplane is introduced.
Using the corepresentation of the quantum group $ SL_q(2)$ a general method for constructing noncommutative spaces covariant under its coaction is developed. The method allows us to treat the quantum plane and Podle\'s' quantum spheres in a…
We consider Laplacians on periodic equilateral metric graphs. The spectrum of the Laplacian consists of an absolutely continuous part (which is a union of an infinite number of non-degenerated spectral bands) plus an infinite number of flat…
In this article, we elucidate the structure and properties of a class of anomalous high-energy states of matter-free $U(1)$ quantum link gauge theory Hamiltonians using numerical and analytical methods. Such anomalous states, known as…
In noncommutative algebraic geometry, noncommutative quadric hypersurfaces are major objects of study. In this paper, we focus on studying noncommutative conics $\operatorname{Proj_{nc}} A$ embedded into Calabi-Yau quantum projective…
In this paper properties of the quantum supermatrices in the quantum supergroup $GL_{p,q}(1|1)$ are discussed. It is shown that any element of $GL_{p,q}(1|1)$ can be expressed as the exponential of a matrix of non-commuting elements, like…
We derive the spectrum of the Laplace-Beltrami operator on the quotient orbifold of the non hyperbolic triangle groups.
Three subgroup type eigenfunctions of the Laplace-Beltrami operator on a two-dimensional two-sheeted hyperboloid are considered and all interbasis expansions between them are calculated. It is shown how the coefficients determining the…
In this work the detailed geometrical description of all possible orthogonal and nonorthogonal systems of coordinates, which allow separation of variables of two-dimensional Helmholtz equation is given as for two-sheeted (upper sheet)…
We study a reduction of deformation parameters in non(anti)commutative N=2 harmonic superspace to those in non(anti)commutative N=1 superspace. By this reduction we obtain the exact gauge and supersymmetry transformations in the Wess-Zumino…
The early idea that a non-perturbative gluon condensate affects the spectrum of heavy quarks is revisited in the light of modern simulation techniques. We evaluate the low lying spectrum of bound states of two heavy quarks for large…
We discuss the non-anticommutative (N=1/2) supersymmetric U(1) gauge theory in four dimensions, including a superpotential. We perform the one-loop renormalisation of the model, including the complete set of terms necessary for…