  We compare the different approaches presently available in literature to
probe the vacuum structure of quantum fields in classical electromagnetic and
gravitational backgrounds. We compare the results from the Bogolubov
transformations and the effective Lagrangian approach with the response of
monopole detectors (of the Unruh-DeWitt type) in non-inertial frames in flat
spacetime and in inertial frames in different types of classical
electromagnetic backgrounds. We also carry out such a comparison in inertial
and rotating frames when boundaries are present in flat spacetime. We find that
the results from these different approaches do not, in general, agree with each
other. We attempt to identify the origin of these differences and then go on to
discuss its implications for classical gravitational backgrounds.
