Related papers: The Ruijsenaars-Schneider Model
This thesis presents our results on Liouville integrable systems of Calogero-Ruijsenaars type: 1. We prove an explicit formula providing canonical spectral coordinates for the rational Calogero-Moser system. 2. We explore action-angle…
Considering the physical 3-space t = constant of the spacetime metrics as spheroidal and pseudo spheroidal, cosmological models which are generalizations of Robertson-Walker models are obtained. Specific forms of these general models as…
Radar-holonomic congruences of wordlines are proposed as a weaker substitute for the too restrictive class of Born-rigid motions. The definition is expressed as a set of differential equations. Integrability conditions and Cauchy data are…
Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly…
We give an overview on the status and on the perspectives of Finsler gravity, beginning with a discussion of various motivations for considering a Finslerian modification of General Relativity. The subjects covered include Finslerian…
An integrable supersymmetric generalization of the trigonometric Ruijsenaars-Schneider model is presented whose symmetry algebra includes the super Poincar\'e algebra. Moreover, its Hamiltonian is showed to be diagonalized by the recently…
Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant ``discrete quantum mechanical systems" are introduced and discussed in some detail. They arise in the problem of…
We discuss various examples of classical Calogero-Moser models with internal degrees of freedom. These models besides of having some attractive properties, like the complete integrability, are of interest eg., in studying spectral…
In this paper we analyze some aspects of the "relativistic glider" proposed by Gu\'eron and Mosna more in detail. In particular an explicit weak gravity and low velocity expansion is presented, the influence of different initial conditions…
It is shown that the groups of Euclidian rotations, rigid motions, proper, orthochronous Lorentz transformations, and the complex rigid motions can be represented by the groups of unit-norm elements in the algebras of real, dual, complex,…
After some recalls on the standard (non)-linear $\sigma$ model, we discuss the interest of B.R.S. symmetry in non-linear $\sigma$ models renormalisation. We also emphasise the importance of a correct definition of a theory through physical…
A general algorithm to construct particle trajectories in 1+1 dimensional canonical relativistic models is presented. The method is a generalization of the construction used in Ruijsenaars-Schneider models and provides a simple proof of the…
The analysis of cylindrical resonators is part of standard physics curricula but, unlike for their rectangular counterpart, their mode structure is hardly ever visualized. The aim of this work is to show a way of doing it, providing a set…
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of…
The aim of this review is to present an overview over available models and approaches to non-commutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold-Moyal spaces and renormalizability, but we will…
An attempt is made to describe the general-relativistic equations of motion for the Schwarzschild geometry in terms of the classical concepts of energy and angular momentum. Using the customary terms the geodesic equations can be viewed in…
A class of theories of gravity based on a Lagrangian which depends on the curvature and metric - but not on the derivatives of the curvature tensor - is of interest in several contexts including in the development of the paradigm that…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
We show that the Calogero and Calogero-Sutherland models possess an N-body generalization of shape invariance. We obtain the operator representation that gives rise to this result, and discuss the implications of this result, including the…
Marginal models involve restrictions on the conditional and marginal association structure of a set of categorical variables. They generalize log-linear models for contingency tables, which are the fundamental tools for modelling the…