Ray Jones

- Review of Lagrangian and Hamiltonian methods in Classical Mechanics.
- The time evolution operator in Quantum Mechanics.
- The Feynman propagator K(2,1)=(x2,t2| x1,t1) and its basic properties: its interpretation via time slicing. The propagator K(i+1,i) for infinitesimal times.
- The Feynman postulates of Quantum Mechanics.
- Steepest descent and stationary phase arguments. The classical limit as (h/2pi)-> 0.
- Relation to the SchrÃ¶dinger equation.
- Propagators for the free particle and harmonic oscillators.
- K(2,1) as a function of energy and its analytic structure. The Feynman-Kac formula. Densities of states.
- Application to perturbation theory and to disordered systems.
- The canonical density matrix in statistical mechanics and its expression as a path integral.
- Calculation of the partition function as a path integral.
- Classical Statistical Mechanics.
- Some comments on many particle systems.
- Description of a polymer chain as a path integral.
- Some problems in optical propagation.

Bibliography