Retarded dispersion forces between molecules

Abstract

The frequency-dependent susceptibility of the molecules and of the electromagnetic field is used to calculate the force between two molecules at zero temperature. The field susceptibility at imaginary frequency, which is the Laplace transform of the retarded potentials, is found from the commutation relations, otherwise we do not need quantum field theory. A method of ‘images’ gives the force between a molecule and a conducting wall, and then we find the susceptibility of the field in the presence of the second molecule. This used to deduce the energy of the first one, and at long distances it turns out to be proportional to the mean square electric field produced by the second molecule. A reduced Hamiltonian involving only the electric and magnetic moments of the molecules gives the simplest proof and agrees with Casimir & Polder’s theory (1948).