Abstract
The covariant methods of Feynman and Dyson are applied to the problem of line shape. It is shown that the line center depends almost completely on the form of the ${{S}_{\mathrm{Fe}}}^{\ensuremath{'}}$ function, that is the Feynman-type Green's function for the electron interacting with an external field ${{A}_{\ensuremath{\mu}}}^{e}$ and with the quantized radiation field. A finite equation for ${{S}_{\mathrm{Fe}}}^{\ensuremath{'}}$ is derived, from which the line center and shape may be calculated to any desired accuracy. The method is illustrated by two examples: the elastic scattering of photons by a one electron atom in its ground state and the emission of photons by the same type of atom following thermal excitation.
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