Coherent radiation of photons by particle wave packets

Abstract

The radiation of photons by electrons is investigated in the framework of quantum electrodynamics up to the second order in the coupling constant e. The N-particle, coherent, and thermal initial states are considered and the forms of the electron wave packets are taken into account. The explicit expressions for the intensity of radiation and the inclusive probability to record a photon are obtained. It is found that there are three processes in this order of perturbation theory where the electron wave packet radiates coherently and can be regarded as a charged fluid even on integrating over the final states of the electron, i.e., in considering the inclusive probabilities and intensity of radiation. These processes are stimulated radiation by an electron, coherent radiation from a beam of particles, and reradiation of a photon in the Compton process. We obtain the explicit expressions for the intensity of radiation and the inclusive probability to record a photon for these processes. As particular cases, we consider: stimulated transition radiation produced by an electron wave packet traversing a mirror and backlighted by a laser wave, reradiation of photons in a coherent state by an electron wave packet. In the latter case, we deduce that the wave packet of a single electron can be endowed with the susceptibility tensor and this tensor has the same form as for an electron plasma in the small recoil limit.

Susceptibility of a single photon wave packet

“…Furthermore, using the formalism developed in Sec. 3, in Appendix B we have generalized the expression for the susceptibility tensor of a single electron wave packet derived in [1] to a nonstationary case.…”

“…This expression coincides with the susceptibility tensor of an electron plasma. Notice that formula (96) is also valid for a single electron wave packet [1].…”

“…The study of the properties inherent to elementary particles such as mass, spin, charges, magnetic and dipole moments, and others is one of the fundamental problems of physics. It was shown in the paper [1] that another one such characteristics of particles is their susceptibility. Staying in line with traditions of classical physics, it appears at first sight that the susceptibility is a property of a group of particles or of particles with nontrivial internal structure.…”

“…Staying in line with traditions of classical physics, it appears at first sight that the susceptibility is a property of a group of particles or of particles with nontrivial internal structure. Nevertheless, as was shown in [1], the susceptibility tensor can be defined, evaluated, and measured experimentally for the wave packet of a single electron. In the present paper, we continue the investigation of susceptibilities of elementary particles and find the susceptibility tensor for the wave packet of a single photon on the photon mass-shell.…”

“…Some calculations arising in evaluating the inclusive probability are removed to Appendix A. In Appendix B, we generalize the expression for the susceptibility tensor of a single electron wave packet obtained in [1] to a nonstationary case.…”