Quantum electrodynamics without potentials

S. Mandelstam

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.

Benliang Li, Daniel William Hewak, Qi Jie Wang

In this article, we start our discussion on the Aharonov-Bohm effect then raise a plausible interpretation within the quantum electrodynamics (QED) framework. We provide a quantum treatment of the source of the electromagnetic potential and argue that the underlying mechanism in AB effect can be viewed as interactions between electrons described by QED theory where the interactions are mediated by virtue photons. On further analysis, we claim that the framework of one particle quantum mechanics (OPQM) can be shown, in general, as a mathematically approximated model which can be reformulated from QED theory. In addition, the classical Maxwell equations are derived from QED scattering process while both classical electromagnetic fields and potentials serve as mathematical tools that are constructed to approximate the interactions among elementary particles described by QED physics, i.e. neither classical fields nor potentials represent any real entities of nature. At the conclusion of this article, we make a few remarks on the hypnosis of the existence of magnetic monopoles.

Navin Khaneja

Carl E. Baum

In this chapter the author explores the degree to which one can measure vector and scalar potentials, including the implications of gauge invariance. Assuming that there are sources (current and/or charge) in some region of space away from the observer, in what sense can the potentials be distinguished? In particular, one can compare static and dynamic conditions. Under static conditions, it is possible to have zero fields in the vicinity of the observer (away from the source region), while having nonzero potentials. These ideas are discussed in this chapter. Two different antennas, one emphasizing the vector potential and the other the scalar potential (Lorenz gauge), are discussed in which the same fields are away from the source region. The author then goes on to consider an alternate way of viewing the role of the vector potential in quantum electrodynamics (QED).