Intense-field quantum electrodynamics in a medium. I. Basic formulation

Abstract

A formalism based on nonrelativistic quantum electrodynamics is developed for the calculation of reaction rates and cross sections for the processes which couple intense fields, such as laser beams, with charged particles in a medium (e.g., plasma). The medium is assumed to be homogeneous, isotropic, and transparent, its linear electromagnetic properties being described by transverse and longitudinal dielectric functions. The Hamiltonian for such a system of charged particles interacting with radiation in the medium is given. The incoming intense fields are described by coherent states, while scattered fields are described by semicoherent states. The theory presented is a diagrammatic perturbation theory for calculating $S$-matrix elements. The Hamiltonian is rearranged by adding and subtracting a single-particle operator (counterterm). A systematic analysis of self-energy structures for charged particles and beam self-energy structures (forward-scattering diagrams of the intense radiation field) is carried out. The self-energy analysis creates a very useful role for the counterterm, endowing it with the ability to renormalize the theory in a specific manner. As an application of the self-energy analysis the counter-term is used to eliminate, to lowest order, the ultraviolet divergence by mass renormalization. Its use in studying beam self-energy structures is also indicated. As an illustration of the formalism, the cross section for Thomson scattering with Doppler shift and the stopping power of a particle generating \ifmmode \check{C}\else \v{C}\fi{}erenkov radiation are calculated.