Derivation of a Transport Equation for Line Radiation Using the Wigner Phase Space Formalism

ABSTRACT

A transport equation for dipole radiation is derived from quantum electrodynamics. The radiation field is described in terms of a space–time Wigner function, which accounts for the position–momentum and time–energy Heisenberg uncertainty relations on an equal footing. The formalism involves the Heisenberg equations of motion for the quantized electric field and the polarization density. It is shown that the radiative transfer equation introduced phenomenologically in textbooks holds at the large spectral band limit, which is characteristic of a slowly varying radiation field in a medium with slowly varying emission and absorption coefficients.

KEYWORDS:

• Photon transport
• radiation transport
• radiative transfer
• transport equation