Foundations. The sum over paths. Path integral representation of the propagator. Short time approximations. Semiclassical limit. The Schrodinger equation from the path integral. Examples: quadratic potentials.
The sign problem. Influence functionals. Harmonic baths and quantum dissipation. Numerical construction of propagators. Discrete variable representations. Iterative evaluation of the path integral. Application: reaction rates.
The linear response approximation. Application: charge transfer in photosynthesis. Influence functionals for anharmonic media. Forward-backward semiclassical dynamics.