Quantum Plasmadynamics by Donald Melrose

Author:Donald Melrose
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(5.6.3)

respectively.

The foregoing argument applies to an electron line connecting an electron in the initial state to an electrons in the final state, and the other possibilities for a single electron line may be treated in a similar manner. For a positron (ε = ε′ =  − 1) line, the foregoing argument applies with primed and unprimed quantities interchanged. For an electron line corresponding to a pair in the initial state, the density of final states is . For an electron line corresponding to a pair in the final state, K z is specified by the initial conditions, and the density of final states factor is .

When there are two or more electron lines, the result (5.6.3) applies separately to each line. For example, consider Møller scattering, where there are two electrons in the initial state, and two electrons in the final state. In the absence of a magnetic field, the details of the scattering depend on the relative positions of the two particles; for example, the scattering angle increases as the distance of closest approach decreases. Nevertheless, in a momentum-space description, the relative position is not specified: the momentum transfer is a free parameter, and it determines both the scattering angle and the distance of closest approach. Thus, the relative position of the scattering particles is not specified independently, but is determined by the theory itself. Similarly, although the relative position of the gyrocenters affects the scattering, in the momentum-space-like description, this relative position is determined by other parameters and does not need to be specified independently.

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