free of ambiguities. The examples encompass classical and quantum phenomena, in relativistic and nonrelativistic conditions. This is a major extension of the quantum-only Aharonov-Bohm effect, both in supporting the primacy of potentials over fields, and also in showing how field-based conceptions can lead to errors in basic applications.'
author:
- 'H. R. Reiss'
title: Ascendancy of potentials over fields in electrodynamics
---

Introduction
============

For most of the history of exploring electromagnetic phenomena, it had been believed that knowledge of the electric and magnetic fields in a physical problem is sufficient to define the problem. The scalar and vector potentials, whose spatial and temporal derivatives yield the fields, had been regarded as auxiliary quantities that are useful but not essential. This conclusion was apparently reinforced by the fact that the set of potentials to represent the fields is not unique. Subject to modest restrictions, there exist transformations (called gauge transformations) to other sets of potentials that produce the same fields.

This seemingly straightforward situation was upset by the Aharonov-Bohm effect [@es; @ab]. The simplest realization of this phenomenon is that an electron beam passing outside a solenoid containing a magnetic field will be deflected, even though there is no field 