Feynman Path Integrals

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 Schrödinger 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.