Geometric Theory of Separation of Variables, Integrability, Superintegrability and Quantization

The MS2Discovery Interdisciplinary Research Institute Seminar

Speaker

Giovanni Rastelli, University of Torino, Italy

Giovanni Rastelli is a researcher in mathematical physics affiliated to the Department of Mathematics of the University of Torino, Italy.

Title

Geometric Theory of Separation of Variables, Integrability, Superintegrability and Quantization

Abstract

The solution of the Hamilton-Jacobi equation of natural Hamiltonian systems, a PDE, can be sometimes obtained by solving a system of separated ODEs in suitable coordinate systems. The geometric theory of separation of variables investigates necessary and sufficient conditions for this task. The same theory characterizes the separability of Helmholtz, Laplace, Schroedinger and Dirac equations. A result of the theory is the characterization of separability in terms of polynomial constants of motion in involution, determining the Liouville integrability of any separable system. The separability in different coordinate systems is often associated with superintegrability, the existence of more constants of motion than necessary for integrability. In recent years, the superintegrability of Hamiltonian systems, and its behaviour in the process of quantization of classical constants of motion, is attracting the interest of many researchers. We review the basis of the theory of separation of variables and its application in recent studies about superintegrabilty and quantization.

Further details are at http://www.ms2discovery.wlu.ca/seminar/18_02_14.html

Refreshments will be provided.

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Date

Wednesday, Feb. 14, 2018

Time

4 p.m.

Location

LH3058 (Lazaridis Hall, Room 3058)