arXiv subjects

Claude Semay

Publications and source records attributed to Claude Semay.

50 records · Page 3Linked to original sources

arXiv2008

Auxiliary field method and analytical solutions of the Schrödinger equation with exponential potentials

The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies and eigenvectors of the Schrödinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schrödinger equation with exponential potentials of the form $-αr^λ\exp(-βr)$ can also be analytically solved by using the auxiliary field method. Formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn on the Yukawa potential and the pure exponential one.

quant-ph↗

arXiv2008

Extensions of the auxiliary field method to solve Schrödinger equations

It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schrödinger equation. This technique can generate the spectrum associated with an arbitrary potential $V(r)$ starting from the analytically known spectrum of a particular potential $P(r)$. In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of $P(r)$. The method is extended in order to find accurate analytical energy formulae for radial potentials of the form $a P(r)+V(r)$, and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed.

quant-ph↗

arXiv2007

Penrose-Carter diagram for an uniformly accelerated observer

An uniformly accelerated observer can build his proper system of coordinates in a delimited sector of the flat Minkowski spacetime. The properties of the position and time coordinate lines for such an observer are studied and compared with the coordinate lines for an inertial observer in a Penrose-Carter diagram for this spacetime.

physics.class-ph↗

arXiv2007

On two- and three-body descriptions of hybrid mesons

Hybrid mesons are exotic mesons in which the color field is not in its ground state. Their understanding deserves interest from a theoretical point of view, because it is intimately related to nonperturbative aspects of QCD. In this work, we analyze and compare two different descriptions of hybrid mesons, namely a two-body $q\bar q$ system with an excited string, or a three-body $q\bar q g$ system. In particular, we show that the constituent gluon approach is equivalent to an effective excited string in the heavy hybrid sector. Instead of a numerical resolution, we use the auxiliary field technique. It allows to find simplified analytical mass spectra and wave functions, and still leads to reliable qualitative predictions. We also investigate the light hybrid sector, and found a mass for the lightest hybrid meson which is in satisfactory agreement with lattice QCD and other effective models.

hep-ph↗

arXiv2006

Covariant oscillator quark model for glueballs and baryons

An analytic resolution of the covariant oscillator quark model for a three-body system is presented. Our harmonic potential is a general quadratic potential which can simulate both a $δ$-shape configuration or a simplified Y-configuration where the junction is located at the center of mass. The mass formulas obtained are used to compute glueball and baryon spectra. We show that the agreement with lattice and experimental data is correct if the Casimir scaling hypothesis is assumed. It is also argued that our model is compatible with pomeron and odderon approaches.

hep-ph↗

arXiv2006

Observer with a constant proper acceleration

Relying on the equivalence principle, a first approach of the general theory of relativity is presented using the spacetime metric of an observer with a constant proper acceleration. Within this non inertial frame, the equation of motion of a freely moving object is studied and the equation of motion of a second accelerated observer with the same proper acceleration is examined. A comparison of the metric of the accelerated observer with the metric due to a gravitational field is also performed.

physics.ed-ph↗

arXiv2005

Casimir scaling, glueballs and hybrid gluelumps

Assuming that the Casimir scaling hypothesis is well verified in QCD, masses of glueballs and hybrid gluelumps (gluon with a point-like $c\bar c$ pair) are computed within the rotating string formalism. In our model, two gluons are attached by an adjoint string in a glueball while the gluon and the colour octet $c\bar c$ pair are attached by two fundamental strings in a hybrid gluelump. Masses for such exotic hadrons are computed with very few free parameters. These predictions can serve as a guide for experimental searches. In particular, the ground state glueballs lie on a Regge trajectory and the lightest $2^{++}$ state has a mass compatible with some experimental candidates.

hep-ph↗

arXiv2004

Light Meson Spectra and Instanton Induced Forces

The spinless Salpeter equation supplemented by an instanton induced force is used to describe the spectra of light mesons, including the pseudoscalar ones. The coupling constants of the instanton induced potential, as well as the quark constituent masses are not treated as simple free parameters but are calculated from the underlying instanton theory. Quite good results are obtained provided the quark are considered as effective degrees of freedom with a finite size. A further test of the model is performed by calculating the electromagnetic mass differences between S-wave mesons.

hep-ph↗

arXiv2004

Universality of Regge and vibrational trajectories in a semiclassical model

The orbital and radial excitations of light-light mesons are studied in the framework of the dominantly orbital state description. The equation of motion is characterized by a relativistic kinematics supplemented by the usual funnel potential with a mixed scalar and vector confinement. The influence of finite quark masses and potential parameters on Regge and vibrational trajectories is discussed. The case of heavy-light mesons is also presented.

hep-ph↗

arXiv2004

Scattering solutions of the spinless Salpeter equation

A method to compute the scattering solutions of a spinless Salpeter equation (or a Schrodinger equation) with a central interaction is presented. This method relies on the 3-dimensional Fourier grid Hamiltonian method used to compute bound states. It requires only the evaluation of the potential at equally spaced grid points and yields the radial part of the scattering solution at the same grid points. It can be easily extended to the case of coupled channel equations and to the case of non-local interactions.

hep-ph↗

arXiv2004

About the Casimir scaling hypothesis

A lattice calculation shows that the Casimir scaling hypothesis is well verified in QCD, that is to say that the potential between two opposite color charges in a color singlet is proportional to the value of the quadratic Casimir operator. On the other hand, in a bag model calculation for the same system, a scaling of the string tension with the square root of the quadratic Casimir operator is obtained. It is shown that, within the same formalism but with the assumption that the width of the string is independent of the color charges, the string tension is proportional to value of the quadratic Casimir operator. Some considerations about the color behavior of the total interaction are given.

hep-ph↗

arXiv2004

Auxiliary fields and the flux tube model

It is possible to eliminate exactly all the auxiliary fields (einbein fields) appearing in the rotating string Hamiltonian to obtain the classical equations of motion of the relativistic flux tube model. A clear interpretation can then be done for the characteristic variables of the rotating string model.

hep-ph↗

arXiv2003

Auxiliary fields and hadron dynamics

The relations existing between the auxiliary field (einbein field) formalism and the spinless Salpeter equation are studied in the case of two particles with the same mass, interacting via a confining potential. The problem of non-orthogonality for radial excited states in the auxiliary field formalism is discussed and found to be non-crucial. It is shown that the classical equations of motion of the rotating string model, derived from the QCD lagrangian, reduce exactly to the classical equations of motion of the phenomenological semirelativistic flux tube model, provided all auxiliary fields are eliminated correctly from the rotating string hamiltonian.

hep-ph↗

arXiv2003

The baryonic Y-shape confining potential energy and its approximants

We discuss the validity of replacing the complicated three-body confinement operator of the Y string junction type by three kinds of approximation which are numerically much simpler to handle: a one-body operator with the junction point at the centre of mass, a two-body operator corresponding to half the perimeter of the triangle formed by the three particles, and the average of both. Two different approaches for testing the quality of the approximations are proposed: a geometrical treatment based on the comparison of the potential energy strengths for the various inter quark distances, and a dynamical treatment based on the comparison of the corresponding effective string tensions using a hyperspherical approach. Both procedures give very similar results. It is shown how to simulate the genuine string junction operator by the approximations proposed above. Exact three-body calculations are presented in order to compare quantitatively the various approximations and to confirm our analysis.

hep-ph↗