相关论文: Segal-Bargmann transform: the $q$-deformation

Following the work in \cite{Mohammed:2012gi}, where the massive ABJM model in 2+1 dimensions was shown to have an abelian reduction to the relativistic Landau-Ginzburg, and motivated by the implications for condensed matter through AdS/CFT,…

This paper presents a derivation of the possible residual symmetries of rational K-matrices which are invertible in the ''classical limit'' (the spectral parameter goes to infinity). This derivation uses only the boundary Yang-Baxter…

We establish a large-deviations principle for the largest eigenvalue of a generalized sample covariance matrix, meaning a matrix proportional to $Z^T \Gamma Z$, where $Z$ has i.i.d. real or complex entries and $\Gamma$ is not necessarily…

We propose a new algebraic deformation of ${\cal N}=4$ SYM via decomposition of spinor and scalar fields in vector supermultiplet. This decomposition generates degrees of freedom of usual quarks and leptons and the deformation model is a…

Deformed correlated Gaussian basis functions are introduced and their matrix elements are calculated. These basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole…

We consider deformations of the differential of a $q$-differential graded algebra. We prove that it is controlled by a generalized Maurer-Cartan equation. We find explicit formulae for the coefficients $c_k$ involved in that equation.

Motivated by the BPS/CFT correspondence, we explore the similarities between the classical $\beta$-deformed Hermitean matrix model and the $q$-deformed matrix models associated to 3d $\mathcal{N}=2$ supersymmetric gauge theories on…

We extend uniform pseudo-Siegel bounds for neutral quadratic polynomials to $\psi^\bullet$-quadratic-like Siegel maps. In this form, the bounds are compatible with the $\psi$-quadratic-like renormalization theory and are easily transferable…

We consider a deformation of Segal-Bargmann space and its transform. We study L^p properties of this transform and obtain entropy-entropy inequalities (Hirschman) and entropy-energy inequalities (log-Sobolev) that generalize the…

In this paper, we introduce a map between the q-deformed gauge fields defined on the GL$_{q}(N) $-covariant quantum hyperplane and the ordinary gauge fields. Perturbative analysis of the q-deformed QED at the classical level is presented…

We consider a natural $q$-deformation of the classical Markov numbers. This $q$-deformation is closely related to $q$-deformed rational numbers recently introduced by two of us. Both notions, those of $q$-rationals and $q$-Markov numbers,…

In complete analogy with Seiberg-Witten map defined in noncommutative geometry we introduce a new map between a q-deformed gauge theory and an ordinary gauge theory. The construction of this map is elaborated in order to fit the Hopf…

We obtain an explicit expression for the defining relation of the deformed W_N algebra, DWA(^sl_N)_{q,t}. Using this expression we can show that, in the q-->1 limit, DWA(^sl_N)_{q,t} with t=e^{-2\pi i/N}q^{(k+N)/N} reduces to the…

The correlated probabilistic model introduced and analytically discussed in Hanel et al (2009) is based on a self-dual transformation of the index $q$ which characterizes a current generalization of Boltzmann-Gibbs statistical mechanics,…

The rules for Yang-Baxter (YB) deformation for a generic Green-Schwarz string sigma model has been obtained recently. We show that the deformation can be described through the action of a coordinate dependent $O(d,d)$ matrix on the target…

The bi-Yang-Baxter sigma-model is a certain two-parameter deformation of the principal chiral model on a real Lie group G for which the left and right G-symmetries of the latter are both replaced by Poisson-Lie symmetries. It was introduced…

We elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work [1]. In the given paper we construct the exact transformations defying the gauge-invariant deformed theory…

The recently discovered general formulas for perturbative correlators in basic matrix models can be interpreted as the Schur-preservation property of Gaussian measures. Then substitution of Schur by, say, Macdonald polynomials, defines a…

In this paper all deformations of the general linear group, subject to certain restrictions which in particular ensure a smooth passage to the Lie group limit, are obtained. Representations are given in terms of certains sets of creation…

We address the issue of generalizing the thermodynamic quantities via $q$-deformation, i.e., via the $q$-algebra that describes $q$-bosons and $q$-fermions. In this study with the application of $q$-deformation to the Landau diamagnetism…