Gauge is Quantum?

Abstract

In this article I discuss a proposed equivalence between quantum mechanics and gauge theory. The evolution of the idea of gauge invariance is very interesting to follow even historically. The idea that gauge transformations have in general no impact on the physics described, leading to even calling gauge variant observables as “unphysical” has transformed quite significantly in the past. Now we know large gauge transformations become sensitive to topological (homotopical) structures of thling group, as is the case of the SU(2) anomaly, and that gauge degrees of freedom do play a role, for example in the problem of confinement, via the Gribov ambiguity. The evolution of the concept of gauge is continued here, by the main claim, that gauge and quantum have equivalent origins and behave similarly to the point that they can be considered dual representations of the same physical ideas.