Theory of Radiation

Recent developments in the theory of radiation have brought this subject to a very complete state. There is a nearly closed domain, in which the interaction between charged particles and the electromagnetic field can be considered as isolated from other phenomena such as mesonic interactions. Within this domain it is now possible to calculate any process with a precision only limited by the labour of the actual calculations. This progress requires for its achievement that quantum field theory should be developed in a relativistically covariant form. The early sections of this review are devoted to a systematic description of the methods of quantization as applied to various matter fields - the scalar meson field considered first for its simplicity, the electromagnetic field and the electron-positron field. Coupled field equations are then discussed, and their solution in the interaction representation is described. The Feynman-Dyson procedure is established for the evaluation of S-matrix elements and applied to typical cases. A general description is given of different methods of renormalization of the S-matrix, and it is shown how this is equivalent to an elimination of unobservable parameters, and a description of phenomena in terms of the (formally infinite) electron mass and charge. A series of individual problems, exhibiting radiative corrections, including the Lamb shift and the anomalous magnetic moment of the electron are considered in more or less detail. Some brief concluding remarks are appended on the development of approximations likely to be useful in meson theory.

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