By van Nieuwenhuizen P.
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The wave function satisfied general Dirac equations, but if one set all times tn equal to the same time t, one came back to Fermi’s and Dirac’s radiation theory. This so-called many-time formalism remains a combination of quantum mechanics for electrons and field theory for photons, but it can describe pair creation if one uses the concept of the Dirac sea. It was shown to be equivalent to earlier approaches , but because it was very complicated, equivalent to other approaches, and a mixture of quantum mechanics and field theory, it was soon abandoned by all physicists, including Dirac himself.
These solutions were a direct consequence of relativity; for example The relativistic wave equation for a scalar field (the “Klein–Gordon equation”) had already been proposed two year earlier . A year later, Pauli proposed a 2-component wave equation for the electron which described spin and which contained the 2 × 2 matrices which bear his name . We discuss the relations between these various approaches in the appendix. 14 1. QED 31 the nonrelativistic 2-component Pauli theory (see the appendix) was free from these “unphysical solutions”.
As early as 1938 he had come to the conclusion that there existed radiative corrections which did not follow from Dirac theory. However, he used a nonrelativistic approach which introduces quadratic divergences (in the relativistic approach, the electron mass has only a logarithmic divergence). In his opinion “the only legitimate starting point for a theory of electrons and radiation was a classical description of an extended electron in a classical electromagnetic field. Both relativity and quantum theory were modifications and refinements grafted onto an essentially classical pictorial world view” .