Logic & Philosophy of Science

Classically, a gauge potential was merely a convenient device for generating a corresponding gauge field. Quantum-mechanically, a gauge potential lays claim to represent an independent aspect of its associated interaction. But it is not clear what this is like or how it is most faithfully represented mathematically. I shall argue that in the theory of electromagnetism (or a non-Abelian generalization) that describes quantum particles subject to a classical interaction, the gauge potential is best understood as a global feature of the physical situation, represented by the holonomies of closed curves in space-time.