Feynman-Kac formula

Feynman-Kac formula: path integral formulation

Goal: Understand one of the most fundamental formulas related to the concept of path integral formulation (which is Feynman-Kac formula) and be familiar with its applications.

Application: Quantum Physics, QFT

Perspective: Immerse into the constructive world of the quantum field theory

Math related to the topic: probability theory, analysis (in particular measure theory)

Scheme:

1. Basics of measure and probability theory
2. Introduction to stochastic processes (random walk, Brownian motion etc.)
3. Diffusion models
4. …

Study team: Marcel Majocha, Adrian Mirecki, Vajda Aniszia

Supervision: Marcin Napiórkowski

Literature:

1. Kac, M. “On distributions of certain wiener functionals.” Transactions of the American Mathematical Society, vol. 65, no. 1, 1949, pp. 1–13
2. Reed, Michael, and Barry Simon. Methods of Modern Mathematical Physics: II: Fourier Analysis, Self-Adjointness. Academic Press, 1975.
3. Moral, Pierre Del. Feynman-Kac Formulae Genealogical and Interacting Particle Systems with Applications. Springer, 2004.
4. Pavliotis, Grigorios A. Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations. Springer, 2014.
5. Kolmogorov, A. N., and S. V. Fomin. Measure, Lebesgue Integrals and Hilbert Space. Academic Press, 1962.

(list will expand during the project)