Related papers: Infrared regular representation of the three dimen…
We consider three-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension, where the upper fluid is bounded above by a rigid lid and the lower fluid is bounded below by a flat bottom. We…
We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In order to avoid the well known instability phenomenon, we consider the so-called Minlos-Faddeev…
We study the Hamiltonian for a system of three identical bosons in dimension three interacting via zero-range forces. In order to avoid the fall to the center phenomenon emerging in the standard Ter-Martirosyan--Skornyakov (TMS)…
In this paper, we consider the cubic nonlinear Schr\"odinger equation with third order dispersion on the circle. In the non-resonant case, we prove that the mean-zero Gaussian measures on Sobolev spaces $H^s(\mathbb{T})$, $s > \frac 34$,…
Neural network representations are often analyzed as vectors in a fixed Euclidean space. However, their coordinates are not uniquely defined. If a hidden representation is transformed by an invertible linear map, the network function can be…
We present a construction of non-Gaussian Borel measures on the space of continuous functions defined on the space of all balls in Euclidean space of arbitrary dimension. These measures induce nets of operator algebras satisfying the…
The affine Gaudin model, associated with an untwisted affine Kac-Moody algebra, is known to arise from a certain gauge fixing of 4-dimensional mixed topological-holomorphic Chern-Simons theory in the Hamiltonian framework. We show that the…
We introduce the Dunkl-Darboux III oscillator Hamiltonian in N dimensions, defined as a $\lambda-$deformation of the N-dimensional Dunkl oscillator. This deformation can be interpreted either as the introduction of a non-constant curvature…
The general class of Robinson-Trautman metrics that describe gravitational radiation in the exterior of bounded sources in four space-time dimensions is shown to admit zero curvature formulation in terms of appropriately chosen…
We consider the Markov random flight $\bold X(t), \; t>0,$ in the three-dimensional Euclidean space $\Bbb R^3$ with constant finite speed $c>0$ and the uniform choice of the initial and each new direction at random time instants that form a…
We classify all subsets $S$ of the projective Hilbert space with the following property: for every point $\pm s_0\in S$, the spherical projection of $S\backslash\{\pm s_0\}$ to the hyperplane orthogonal to $\pm s_0$ is isometric to…
We justify that homodyne tomography turns out to be informationally complete when the number of independent quadrature measurements is equal to the dimension of the density matrix in the Fock representation. Using this as our thread, we…
The two-dimensional Ising model is representable as a lattice free-fermion field theory in terms of the integral over anticommuting Grassmann variables. The exact solution in a zero magnetic field then follows by evaluating Gaussian…
The paper interprets the cubic nonlinear Schr\"odinger equation as a Hamiltonian system with infinite dimensional phase space. There is a Gibbs measure which is invariant under the flow associated with the canonical equations of motion. The…
An N-dimensional position-dependent mass Hamiltonian (depending on a parameter \lambda) formed by a curved kinetic term and an intrinsic oscillator potential is considered. It is shown that such a Hamiltonian is exactly solvable for any…
We present a tensor formulation for free compact electrodynamics in three Euclidean dimensions and use this formulation to construct a quantum Hamiltonian in the continuous-time limit. Gauge-invariance is maintained at every step and the…
We analyse the non-linear gravitational dynamics of a pressure-less fluid in the Newtonian limit of General Relativity in both the Eulerian and Lagrangian pictures. Starting from the Newtonian metric in the Poisson gauge, we transform to…
We solve a system of massless fermions constrained to two space-time dimensions interacting via a $d$ space-time dimensional Maxwell field. Through dimensional reduction to the defect and bosonization, the system maps to a massless scalar…
We consider a class of gauge invariant models on the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of $\mathbb{R}^3$. Focusing on massless models with no linear $A_i$ dependence, we obtain noncommutative gauge models for which…
We introduce a complete gauge fixing for cylindrical spacetimes in vacuo that, in principle, do not contain the axis of symmetry. By cylindrically symmetric we understand spacetimes that possess two commuting spacelike Killing vectors, one…