New York University, USA
Ontological Clarity, Electromagnetism and the Aharanov-Bohm Effect
Mathematical physics uses abstract mathematical structures to represent physical states of the world. But the physical world is not literally made of those mathematical structures, so there must be some account of how the mathematics is to be understood. This requires a clear statement of the physical ontology postulated by a theory and a commentary on how the mathematical degrees of freedom correspond (or fail to correspond) to the physical degrees of freedom.
Classical electro-magnetic theory provides a wonderful illustration of this point. I will offer a disciplined way to present the ontological and nomological commitments of a theory, and show how many different physical theories can be associated with one and the same mathematical formalism. I will then discuss the bearing of the Aharonov-Bohm effect on the choice among this multiplicity.