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.
Study Team: Marcel Majocha, Adrian Mirecki, Aniszia Vajda, Alex Muresan
Supervision: Marcin Napiórkowski
Application: Quantum Physics, QFT
Perspective: Immerse into the constructive world of quantum field theory
Math related to the topic: probability theory, analysis (in particular measure theory)
Logical scheme:
- Basics of measure and probability theory
- Introduction to stochastic processes (random walk, Brownian motion etc.)
- Diffusion models
- …
Literature:
- Kac, M. “On distributions of certain wiener functionals.” Transactions of the American Mathematical Society, vol. 65, no. 1, 1949, pp. 1–13
- Moral, Pierre Del. Feynman-Kac Formulae Genealogical and Interacting Particle Systems with Applications. Springer, 2004.
- Pavliotis, Grigorios A. Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations. Springer, 2014.
- Kolmogorov, A. N., and S. V. Fomin. Measure, Lebesgue Integrals and Hilbert Space. Academic Press, 1962.
(list will expand during the project)