Quantum interference and the classical limit

Abstract

A relationship between the quantum phase shift due to an external field in an (infinitesimal) two-beam interference experiment and the classical transverse acceleration, previously given by the author, is generalized covariantly and the phase shift associated with the longitudinal acceleration is deduced. This relation implies that the mass of a spinless elementary particle is a constant of motion, even in the presence of external fields in a curved space-time. Also according to this relation, the infinitesimal Aharonov-Bohm effect is equivalent to the Lorentz force law. The case of a charged particle moving in the electromagnetic field due to electric and magnetic charges obeying Dirac's quantization condition is treated and a prescription is given for constructing its quantum mechanical wave function directly from the classical equation of motion, using path integrals, without requiring a knowledge of the Lagrangian or Hamiltonian of the interaction. Generalization to an arbitrary gauge field is briefly considered and a theorem is proven which implies that the holonomy transformations (path-ordered operators that parallel transport around closed curves) at an arbitrary space-time point contain all the gauge-invariant information of a gravitational or gauge field connection.