Force-Free Interactions and Nondispersive Phase Shifts in Interferometry

Zeilinger's observation that phenomena of the Aharonov-Bohm type lead to nondispersive, i.e. energy-independent, phase shifts in interferometers is generalized in a new proof which shows that the precise condition for nondispersivity is a force-free interaction. The converse theorem is disproved by a conceptual counter example. Applications to several nondispersive interference phenomena are reviewed briefly. Those fall into two classes which are objectively distinct from each other in that in the first class phase shifts depend only on the topology of the interfering beam paths while in the second class force-free physical interactions take place at identifiable points along the path. Apparent disagreements in the literature about the topological nature of the phenomena in the second class stem from differing definitions.