UVictoria Dynamics and Probability Seminar: Yu-Ting Chen

Feynman’s path integral expresses the probability amplitude of a quantum mechanical system as a “sum of trajectories” of the classical system. Since this integral has not been given a satisfactory mathematical meaning, a widely accepted treatment is M. Kac’s method which starts with the idea of rotating “real time” to “imaginary time.” The corresponding path integrals are stochastic, given by exponential functionals of Brownian motion.

This talk will introduce a Feynman–Kac-type formula given by a non-exponential multiplicative functional of a non-Gaussian process. The formula represents the many-body delta-Bose gas in two dimensions, extending technically the two-body case obtained earlier. To contrast the classical and new, for this seminar, a significant part of the talk will discuss the classical Feynman–Kac formula.