Theory of the External Field
The theory which we have developed up to this point is completely general in the sense that it describes all the known physical processes which are caused by the interaction of electrons with photons. In particular, it contains as limiting cases the properties of classical charge and current distributions. The transition to the classical limiting case is carried out essentially by going from the operator relations to the relations between expectation values of these operators. In this transition the operators a µ and ψ behave quite differently. While the expectation value (a µ ) of a µ corresponds to the classical electromagnetic vector potential, there is no quantity in the classical picture which corresponds to (ψ). Only bilinear expressions of ψ operators, such as (ψγ µ ψ), have a classical interpretation.
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