The MS2Discovery Interdisciplinary Research Institute Seminar
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.
Geometric Theory of Separation of Variables, Integrability, Superintegrability and Quantization
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 https://www.ms2discovery.wlu.ca/seminar/18_02_14.html.
Refreshments will be provided.
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