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Physical Review

Electromagnetic Potentials in Quantum Mechanics

Henri E. Mitler

Published Nov 1, 1961• 6 citations
Publisher

Abstract

Electromagnetic potentials are found to be significant in quantum theory, even when the fluctuations of the vacuum are taken into account. Conditions are found under which the fluctuations will, nevertheless wash out an interference pattern.
DOI
10.1103/physrev.124.940

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Significance of Electromagnetic Potentials in the Quantum Theory

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In this paper, we discuss some interesting properties of the electromagnetic potentials in the quantum domain. We shall show that, contrary to the conclusions of classical mechanics, there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish. We shall then discuss possible experiments to test these conclusions; and, finally, we shall suggest further possible developments in the interpretation of the potentials.

Physical Review•Aug 1, 1959•6,995 citations
In this article, we discuss in further detail the significance of potentials in the quantum theory, and in so doing, we answer a number of arguments that have been raised against the conclusions of our first paper on the same subject. We then proceed to extend our treatment to include the sources of potentials quantum-mechanically, and we show that when this is done, the same results are obtained as those of our first paper, in which the potential was taken to be a specified function of space and time. In this way, we not only answer certain additional criticisms that have been made of the original treatment, but we also bring out more clearly the importance of the potential in the expression of the local character of the interaction of charged particles and the electromagnetic field.
The effects of the scalar and vector potentials in quantum mechanics, which were pointed out recently by Aharonov and Bohm, are discussed from the point of view of the consistency of the quantum-mechanical description of interference experiments. A well-known requirement for this consistency is that if any measuring device is introduced that can be used to determine which path the particle has taken, it must have the effect of eliminating the interference phenomenon. Two conceptual experiments are discussed, corresponding to the two phase effects noted by Aharonov and Bohm. In each case it is found that the phase effect is of just the magnitude required to destroy the interference pattern when the circumstances are such that no pattern should be observed.
Abstract We have developed a linearized effective theory with quantum mechanical Gaussian wavepacket of a charged relativistic particle coupled to quantum electromagnetic fields at a scale well below the Schwinger limit. Using this effective theory, we study the quantum decoherence of single electrons at rest due to their interactions with electromagnetic vacuum. According to the existing data of electron interference experiments in electron microscopes, the values of the parameters in our effective theory are chosen. With these values, we find that weak decoherence by vacuum fluctuations may have blurred the interference pattern in Ref. [1].
In this paper, we discuss some interesting properties of the electromagnetic potentials in the quantum domain. We shall show that, contrary to the conclusions of classical mechanics, there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish. We shall then discuss possible experiments to test these conclusions; and, finally, we shall suggest further possible developments in the interpretation of the potentials.