Second order quantum corrections to the classical reflection factor of the sinh-Gordon model

The sinh-Gordon model on a half-line with integrable boundary conditions is considered in low order perturbation theory developed in affine Toda field theory. The quantum corrections to the classical reflection factor of the model are studied up to the second order in the difference of the two boundary parameters and to one loop order in the bulk coupling. It is noticed that the general form of the second order quantum corrections are consistent with Ghoshal's formula.Comment: 24 pages and 1 figure. LaTex2

On the quantum reflection factor for the sinh-Gordon model with general boundary conditions

The one loop quantum corrections to the classical reflection factor of the sinh-Gordon model are calculated partially for general boundary conditions. The model is studied under boundary conditions which are compatible with integrability, and in the framework of the conventional perturbation theory generalized to the affine Toda field theory. It is found that the general form of the related quantum corrections are hypergeometric functions.Comment: 32 pages and 1 figure. LaTex2

First order quantum corrections to the classical reflection factor of the sinh-Gordon model

The sinh-Gordon model is restricted to a half-line by boundary conditions maintaining integrability. A perturbative calculation of the reflection factor is given to one loop order in the bulk coupling and to first order in the difference of the two parameters introduced at the boundary, providing a further verification of Ghoshal's formula. The calculation is consistent with a conjecture for the general dependence of the reflection factor on the boundary parameters and the bulk coupling.Comment: 16 pages, 1 figur

Klein-Gordon Equation with Superintegrable Systems: Kepler-Coulomb, Harmonic Oscillator, and Hyperboloid

We study the two-dimensional Klein-Gordon equation with spin symmetry in the presence of the superintegrable potentials. On Euclidean space, the SO(3) group generators of the Schrödinger-like equation with the Kepler-Coulomb potential are represented. In addition, by Levi-Civita transformation, the Schrödinger-like equation with harmonic oscillator which is dual to the Kepler-Coulomb potential and the SU(2) group generators of associated system are studied. Also, we construct the quadratic algebra of the hyperboloid superintegrable system. Then, we obtain the corresponding Casimir operators and the structure functions and the relativistic energy spectra of the corresponding quasi-Hamiltonians by using the quadratic algebra approach

Saw tooth cardiomyopathy: a case report

Saw tooth cardiomyopathy is an unusual and rare type of left ventricular dysplasia that is characterized by multiple projections of compacted myocardium that makes the appearance of �saw tooth� in noninvasive imaging. We present a young man with signs and symptoms of heart failure and reduced left ventricular function in echocardiography who showed distinctive left ventricle features of saw tooth cardiomyopathy (saw tooth appearance of myocardium in basal inferolateral and basal to mid lateral segments) in cardiac magnetic resonance imaging. © 2020 The Authors. ESC Heart Failure published by John Wiley & Sons Ltd on behalf of the European Society of Cardiology

Form factors of boundary fields for A(2)-affine Toda field theory

In this paper we carry out the boundary form factor program for the A(2)-affine Toda field theory at the self-dual point. The latter is an integrable model consisting of a pair of particles which are conjugated to each other and possessing two bound states resulting from the scattering processes 1 +1 -> 2 and 2+2-> 1. We obtain solutions up to four particle form factors for two families of fields which can be identified with spinless and spin-1 fields of the bulk theory. Previously known as well as new bulk form factor solutions are obtained as a particular limit of ours. Minimal solutions of the boundary form factor equations for all A(n)-affine Toda field theories are given, which will serve as starting point for a generalisation of our results to higher rank algebras.Comment: 24 pages LaTeX, 1 figur

Coherent states for exactly solvable potentials

A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is given. The method, {\it a priori}, is potential independent and connects with earlier developed ones, including the oscillator based approaches for coherent states and their generalizations. This approach can be straightforwardly extended to construct more general coherent states for the quantum mechanical potential problems, like the nonlinear coherent states for the oscillators. The time evolution properties of some of these coherent states, show revival and fractional revival, as manifested in the autocorrelation functions, as well as, in the quantum carpet structures.Comment: 11 pages, 4 eps figures, uses graphicx packag