Selfconsistent frequencies of the electronphoton system
Abstract
The Heisenberg equations describing the dynamics of coupled Fermion photon operators are solved selfconsistently. Photon modes, for which ω~=kc, and particlelike Bohr modes with frequencies ω_{nI}~=(E_{n}E_{I})/ħ are both approximate solutions to the system of equations that results if the current density is the source in the operator Maxwell equations. Current fluctuations associated with the Bohr modes and required by a fluctuationdissipation theorem are attributed to the point nature of the particle. The interaction energy is given by the Casimirforcelike expression ∆E=1/2ħtsum(∆ω_{nI}+∆ω_{kc}) or by the expectation value of 1/2(qcphiqp^.A^/mc+q^{2}A^{2}/mc^{2}). It is verified that the equaltime momentumdensity and vectorpotential operators commute if the contributions of both the Bohr modes and vacuum fluctuations are included. Both electromagnetic and Bohr or radiationreaction modes are found to contribute equally to spontaneous emission and to the Lamb shift.
 Publication:

Physical Review A
 Pub Date:
 September 1993
 DOI:
 10.1103/PhysRevA.48.1824
 Bibcode:
 1993PhRvA..48.1824H
 Keywords:

 03.65.Bz;
 12.20.m;
 Quantum electrodynamics