  Electromagnetic vector potential has physical significance in quantum
mechanics as revealed by the Aharonov-Bohm effect for charged particles.
However, till date it is thought that we cannot measure the vector potential
directly as this is not a gauge invariant quantity. Contrary to this belief,
here we show that one can indeed measure the electromagnetic vector potential
using the notion of weak value. We show that it is simply the difference
between the weak value of the canonical momentum of a charged particle in the
presence and absence of magnetic field. This suggests that the vector potential
is not only a physical entity but can be measured directly in the experiment.
