arXiv subjects
Publications and source records attributed to Michel Talon.
We study the Kowalevski expansions near singularities of the swinging Atwood's machine. We show that there is a infinite number of mass ratios $M/m$ where such expansions exist with the maximal number of arbitrary constants. These expansions are of the so--called weak Painlevé type. However, in view of these expansions, it is not possible to distinguish between integrable and non integrable cases.
We extend the semiclassical study of the Neumann model down to the deep quantum regime. A detailed study of connection formulae at the turning points allows to get good matching with the exact results for the whole range of parameters.
We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.
We study numerically the spectrum and eigenfunctions of the quantum Neumann model, illustrating some general properties of a non trivial integrable model.
These lectures present some basic facts in field theory necessary to understand the quantum theory of the Standard Model of weak and electromagnetic interactions.