On a Formulation of Quantum Electrodynamics

Vladimir D. Skarzhinsky

Edward B. Manoukian

Yakir Aharonov, David Böhm

In this article, we reply to a suggestion of DeWitt for formulating a nonlocal quantum electrodynamics without potentials, showing that his proposal is not a real elimination of potentials, but only a substitution with the aid of which the essential role of potentials is somewhat obscured. Thus, we are not led to change our conclusion that potentials are significant in the formulation of quantum electrodynamics. We do, however, discuss some of the conditions that would have to be satisfied by an essentially nonlocal electrodynamics, and show that such a theory, if it could be developed, would very probably bring about profound modifications in the forms of the laws of quantum mechanics.

M. I. Shirokov

The fulfillment in quantum electrodynamics of the principle of relativistic causality—the signal velocity does not exceed the velocity of light—is discussed. In Sec. 1 it is argued that this principle is not guaranteed automatically merely by the local commutativity of the theory. Section 2 is a critical review of the signal transmission problems which have been formulated and solved in the literature. In Sec. 3, this problem is considered in the framework of a simple but fairly realistic model of quantum electrodynamics. The signal source is an external current localized in some region S. The arrival of a signal in a region D at a distance R is established by a change in the coordinate, momentum, or energy of a charged particle. It is shown that proof of relativistic causality of the theory requires one to take into account appropriately quantum-mechanical and, in particular, quantum-electrodynamical features of the problem. In the final fourth section, a general formulation and exact solution of the signal transmission problem are given. The treatment is of sufficient generality for one to be able to assert that in the framework of quantum electrodynamics none of the possible methods of signal transmission violate relativistic causality.

Oscar Wallace Greenberg

V. A. Golovko

In a previous paper by the author a new approach in quantum electrodynamics was proposed in which the electronic and electromagnetic fields are ordinary c-numbers in contradistinction to noncommuting q-numbers used in the standard formulation of quantum electrodynamics. The factual development of standard quantum electrodynamics began when the anomalous correction to the electron magnetic moment and the Lamb shift were calculated and the calculations were confirmed by experiment. It is demonstrated in the present paper how the anomalous electron magnetic moment and Lamb shift can be obtained in the new approach in quantum electrodynamics.