K. Ilinski: Key results in physics and mathematics

Functional integral representation of classical mechanics: new correspondence between integrable classical systems in arbitrary dimensions and exactly solvable functional integrals

Rewriting classical Liouville picture in terms of quantum objects one can use full machinery of quantum field theory to examine complex problems of classical mechanics. As a byproduct we found that any integrable classical system in arbitrary dimensions corresponds to a new class of exactly solvable quantum systems and explicitely calculated non-trivial functional integrals. One can use this result as a new method to calculate functional integrals by mapping it in a corresponding classical system.

Anton Zherebtsov and Kirill Ilinski, “New application of functional integrals to classical mechanics”, Phys.Lett. A 335 (2005), 337-346

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