Path integrals and statistical mechanics

This lecture covers the basics of path integral methods in statistical mechanics, focusing on the partition function in the position representation and the quantum canonical partition function. Mariana Rossi from MPI for the Structure and Dynamics of Matter explains the Trotter factorization and its application to Hamiltonians with arbitrary potentials, as well as the quantum-classical isomorphism. The lecture also delves into multidimensional generalization for distinguishable particles and properties of the ring polymer, emphasizing the temperature dependence on the evolution of each bead. Sampling techniques within this framework are also discussed.