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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 {S₅₄}^' function, that is the Feynman-type Green's function for the electron interacting with an external field {A_}^e and with the quantized radiation field. A finite equation for {S₅₄}^' 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.
F. E. Low (1952) studied this question.
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