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We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed…
The von Neumann equation with delta self-interaction kernel serves as a statistical model for nonlinear waves, and it exhibits a bifurcation between stable and unstable regimes. In oceanography it is known as the Alber equation, and its…
We define and study the properties of Darboux-type transformations between Sturm--Liouville problems with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary…
Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of…
The Linet-Tian metrics are solutions of the Einstein equations with a cosmological constant, $\Lambda$, that can be positive or negative. The linear instability of these metrics in the case $\Lambda <0$, has already been established. In the…
Let $\left(\mathcal{H},\left(.,.\right)\right)$ be a Hilbert space and let $\mathcal{L}\left(\mathcal{H}\right)$ be the linear space of bounded operators in $\mathcal{H}$. In this paper, we deal with $\mathcal{L}(\mathcal{H})$-valued…
Given a purely contractive matrix-valued analytic function $\Theta$ on the unit disc $\bm{D}$, we study the $\mc{U} (n)$-parameter family of unitary perturbations of the operator $Z_\Theta$ of multiplication by $z$ in the Hilbert space…
A Procedure is outlined that may be used as a starting point for a perturbative treatment of theories with permanent confinement. By using a counter term in the Lagrangian that renormalizes the infrared divergence in the Coulomb potential,…
Perturbative QFT is developed in terms of off-shell fields (that is, functionals on the configuration space not restricted by any field equation), and by quantizing the (underlying) free theory by an $\hbar$-dependent deformation of the…
To solve the quantum-mechanical problem the procedure of mapping onto linear space $W$ of generators of the (sub)group violated by given classical trajectory is formulated. The formalism is illustrated by the plane H-atom model. The problem…
The algebraic approach to operator perturbation method has been applied to two quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator'' and ``The Generalized Zeeman Effect''. To that end, two realizations of the…
We show that natural noncommutative gauge theory models on $\mathbb{R}^3_\lambda$ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of $\mathbb{R}^3_\lambda$ and the components of…
We study the crystalline phase of the $O(2N)$ Gross--Neveu model with a chemical potential for $a \leq N-2$ of the fermions. We analyze the problem in three independent ways: using perturbative QFT methods, a semiclassical large $N$…
We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…
This paper addresses inverse problems (in a broad sense) for two classes of multivariate neural network (NN) operators, with particular emphasis on saturation results, and both analytical and semi-analytical inverse theorems. One of the key…
We study the quantum Riemann-Hilbert problems determined by the refined Donaldson-Thomas theory on the resolved conifold. Using the solutions to classical Riemann-Hilbert problems by Beidgeland, we give explicit solutions in terms of…
Given a complex, elliptic coefficient function we investigate for which values of $p$ the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly…
In this article, a characterization of the class of Herglotz-Nevanlinna functions in $n$ variables is given in terms of an integral representation. Furthermore, alternative conditions on the measure appearing in this representation are…
We derive an integral representation for Herglotz-Nevanlinna functions in two variables which provides a complete characterization of this class in terms of a real number, two non-negative numbers and a positive measure satisfying certain…
A parameter dependent perturbation of the spectrum of the scalar Laplacian is studied for a class of nonlocal and non-self-adjoint rank one perturbations. A detailed description of the perturbed spectrum is obtained both for Dirichlet…