The Algebra & Geometry of Modern Physics

I will introduce Feynman path integral approach to Quantum Mechanics, focusing on a few simple examples: free particle, a particle coupled to magnetic field, and a general lagrangian quadratic in positions and velocities. Feynman heuristic idea will be presented as well as rigorous (but with imaginary time evolution) approach using Feynman-Kac formula. A partition function for the Simple Harmonic Oscilator will be computed using the path integral.