Dissipation in the Klein-Gordon Field

The formalism of (±)-frequency parts , previously applied to solution of the D'Alembert equation in the case of the electromagnetic field, is applied to solution of the Klein-Gordon equation for the K-G field in the presence of sources. Retarded and advanced field operators are obtained as solutions, whose frequency parts satisfy a complex inhomogeneous K-G equation. Fourier transforms of these frequency parts are solutions of the central equation, which determines the time dependence of the destruction/creation operators of the field. The retarded field operator is resolved into kinetic and dissipative components. Correspondingly, the energy/stress tensor is resolved into three components; the power/force density, into two—a kinetic and a dissipative component. As in the analogous electromagnetic case the dissipation theorem is derived according to which work done by the dissipative power/force is negative: energy/momentum is dissipated from the sources to the K-G field. Boson quantization conditions are satisfied by the kinetic component but not by the dissipative component of the retarded K-G field.