Physical Review

Quantum Electrodynamics without Dead Wood

P. A. M. Dirac

Published Aug 9, 1965• 55 citations

Abstract

In quantum electrodynamics one can obtain a Hamiltonian which gives reasonable field equations in the Heisenberg picture, but which does not allow of solutions of the wave equation to represent physical states in the Schr\"odinger picture. The inference is that the Heisenberg picture is a good picture, the Schr\"odinger picture is a bad picture, and the two pictures are not equivalent. The usual proof of the equivalence of the two pictures fails because the state vector of the Schr\"odinger picture does not remain in Hilbert space. One can set up quantum electrodynamics entirely in the Heisenberg picture and thereby avoid the worst difficulties encountered in the Schr\"odinger picture. The theory takes a logical form and is not merely an assembly of working rules. It can be applied to the calculation of the anomalous magnetic moment and the Lamb shift, and is then similar to the usual calculations of these effects, with a good deal of dead wood cut away. There is a problem concerned with the general interpretation of quantum mechanics when one cannot use the Schr\"odinger picture and some postulates are proposed for dealing with it.

DOI: 10.1103/physrev.139.b684

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