  In a standard interferometry experiment, one measures the phase difference
between two paths by recombining the two wave packets on a beam-splitter.
However, it has been recently recognized that the phase can also be estimated
via local measurements, by using an ancillary particle in a known superposition
state. In this work, we further analyse these protocols for different types of
particles (bosons or fermions, charged or uncharged), with a particular
emphasis on the subtleties that arise when the phase is due to the coupling to
an abelian gauge field. In that case, we show that the measurable quantities
are spacetime loop integrals of the 4-vector potential, enclosed by two
identical particles or by a particle-antiparticle pair. Furthermore, we
generalize our considerations to scenarios involving an arbitrary number of
parties performing local measurements on a general charged fermionic state.
Finally, as a concrete application, we analyse a recent proposal by Marletto
and Vedral (arXiv:1906.03440) involving the time-dependent Aharonov-Bohm
effect.
