A relativistic quantum theory for processes in collisionless plasmas

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Abstract
The theory reduces to that for a classical collisionless plasma in the classical limit and to conventional quantum electrodynamics in vacuo. The generalization involves two stages. The first is the use of quantum electrodynamics to calculate the linear and non-linear responses of an electron gas. Explicit expressions are derived for the linear response in a static magnetic field, and for the lowest order non-linear response in the absence of a static magnetic field. The second stage involves a generalization of the conventional diagrammatic technique to include the effects of the non-linear responses of the medium. Additional diagrammatic structures called multiple-photon vertices are introduced. Rules are given for drawing the generalized diagrams and for writing down the associated amplitudes. Illustrative examples are given.