We compare the different approaches presently available in literature toprobe the vacuum structure of quantum fields in classical electromagnetic andgravitational backgrounds. We compare the results from the Bogolubovtransformations and the effective Lagrangian approach with the response ofmonopole detectors (of the Unruh-DeWitt type) in non-inertial frames in flatspacetime and in inertial frames in different types of classicalelectromagnetic backgrounds. We also carry out such a comparison in inertialand rotating frames when boundaries are present in flat spacetime. We find thatthe results from these different approaches do not, in general, agree with eachother. We attempt to identify the origin of these differences and then go on todiscuss its implications for classical gravitational backgrounds.
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