  The usual, "static" version of the quantum Zeno effect consists in the
hindrance of the evolution of a quantum systems due to repeated measurements.
There is however a "dynamic" version of the same phenomenon, first discussed by
von Neumann in 1932 and subsequently explored by Aharonov and Anandan, in which
a system is forced to follow a given trajectory. A Berry phase appears if such
a trajectory is a closed loop in the projective Hilbert space. A specific
example involving neutron spin is considered and a similar situation with
photon polarization is investigated.
