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.
Giovanni Rastelli is a researcher in mathematical physics affiliated
to the department of mathematics of the university of Torino, Italy.
Contact at the MS2Discovery Research Institute: Manuele Santoprete (Host of the speaker, Tecton 3)
Refreshments will be provided