Unifying interpretations of the Gouy phase anomaly for electron waves

We provide a unified description of the Gouy phase anomaly, highlighting the pivotal role of local fluctuations in transverse momentum and quantal phase changes associated with electron trajectories that touch caustics. Using arguments based on wave optics, at the interface between classical and quantum mechanics, we derive the magnitude of the quantized Gouy phase changes for scalar waves. Our analysis unifies disparate descriptions of the Gouy anomaly within a single theoretical framework. In particular, we find that the phase anomaly connects Maslov indices, quantal Berry phases, Heisenberg momentum fluctuations, and confinement-induced Lévy-Leblond phase shifts.