A student learns to build the quantum time-evolution amplitude as a sum over histories weighted by exp(iS), starting from Feynman-Dirac time slicing and the Gaussian and Fresnel integrals that make it computable. From there the same object is carried through semiclassical expansion and functional determinants, Euclidean rotation to the partition function of statistical mechanics, coherent states and Grassmann variables for bosons and fermions, and finally generating functionals, Feynman diagrams, gauge fixing with Faddeev-Popov ghosts, and Monte Carlo evaluation on a Euclidean lattice. The unifying skill is recognising one formalism behind quantum mechanics, many-body physics, and quantum field theory, and knowing which approximation (saddle point, variational, perturbative, or numerical) each problem calls for.
This is a comprehensive graduate-level lecture series by R. Rosenfelder covering path integral methods across quantum mechanics, many-body physics, and quantum field theory. The material includes det…