On the physical significance of the vector potential

R. Carles, Olivier Pujol, José-Philippe Pérez

Yakir Aharonov, Gideon Carmi

Shi Jian-xi

Electromagnetic AB effect,which is a significant discovery of physics,brings a huge impact to classical physics.The understanding of vector potential is the key for understanding the microscopic electromagnetic effect.This paper introduces the basic concepts of electromagnetic AB effect and vector potential in electromagnetic field.

Robert Golub, J. P. Carrico, T. S. Stein +1 more

Arun Kumar Pati

Electromagnetic vector potential has physical significance in quantum mechanics as revealed by the Aharonov-Bohm effect for charged particles. However, till date it is thought that we cannot measure the vector potential directly as this is not a gauge invariant quantity. Contrary to this belief, here we show that one can indeed measure the electromagnetic vector potential using the notion of weak value. We show that it is simply the difference between the weak value of the canonical momentum of a charged particle in the presence and absence of magnetic field. This suggests that the vector potential is not only a physical entity but can be measured directly in the experiment.

Jing‐Ling Chen, Xing-Yan Fan, Xiang-Ru Xie

The Aharonov-Bohm (AB) effect is an important discovery of quantum theory. It serves as a surprising quantum phenomenon in which an electrically charged particle can be affected by an electromagnetic potential, despite being confined to a region in which both the magnetic field and electric field are zero. This fact gives the electromagnetic potentials greater significance in quantum physics than in classical physics. The original AB effect belongs to an “electromagnetic type”. A certain vector potential is crucial for building a certain type of AB effect. In this work, we focus on the “spin”, which is an intrinsic property of microscopic particles that has been widely accepted nowadays. First, we propose the hypothesis of spin vector potential by considering a particle with a spin operator. Second, to verify the existence of such a spin vector potential, we present a gedanken double-slit interference experiment (i.e., the spin AB effect), which is possible to be observed in the lab. Third, we apply the spin vector potential to naturally explain why there were the Dzyaloshinsky-Moriya-type interaction and the dipole-dipole interaction between spins, and also predict a new type of spin-orbital interaction.