Juan J. Morales-Ruiz 氏 (Universidad Politecnica de Madrid, Spain)
2022年10月13日(木) 16時00分
総合研究10号館317号室 / Zoom会議 (ハイブリッド)
In my 2020 paper on Differential Galois Theory and Path Integrals, I pointed out that a well-known object of classical mechanics, the variational equation, becomes the key to solve the semiclassical (or WKB) approximation in the corresponding problem in Quantum Mechanics. The connection with Differential Galois Theory is given by a joint result with Jean-Pierre Ramis obtained more than 22 years ago. Then, if the classical system is integrable, the semiclassical approach must be obtained in closed form, i.e., it can be considered as integrable as well. This talk will be mainly devoted to give some idea of the many open problems motivated by the above simple result: problems from Quantum Mechanics to Quantum Field Theory. We are working on several of these problems.