 where \(A_{\mu}\) is the electromagnetic potential at spacetime point \(x^{\mu}\), e is the particles’ charge, and the integral is taken over each closed loop C in spacetime. This can be seen as an instance of the more general notion of the holonomy of a closed curve, a notion that has come to the fore in contemporary formulations of gauge theories including electromagnetism in terms of fiber bundles (Healey (2007)). Applied to the Aharonov-Bohm case, this means that the constant magnetic field is accompanied by an association of a phase factor \(S(C)\) with all closed curves C in space, where \(S(C)\) is defined by