PATH INTEGRATION AND STATISTICAL FIELD THEORY IN THE CLASSICAL REGIME

It’s well known that path integration is a powerful tool, shown by Richard Feynman to be capable of deriving the Schrodinger equation and canonical commutation relations. Perhaps lesser known is that this method is highly useful for classical systems subject to thermal fluctuations. In this talk, the path integral is first derived quantum mechanically. It’s then used in the classical regime to calculate the propagator of the Ornstein-Uhlenback process. Finally, the dielectrophoretic susceptibility is derived using statistical field theory on a spherical cavity in a polarizable material subject to Gaussian fluctuations (such as a hard sphere in liquid water) under the influence of an applied electric field.