Probes of the vacuum structure of quantum fields in classical backgrounds

TL;DR

This paper compares various methods for probing the vacuum structure of quantum fields in classical backgrounds, revealing discrepancies among approaches and discussing their implications for gravitational settings.

Contribution

It systematically compares multiple approaches to vacuum structure analysis, highlighting their differences and exploring the origins and implications of these discrepancies.

Findings

Different approaches often yield inconsistent results.

Discrepancies depend on the frame of reference and boundary conditions.

Implications for quantum field theory in gravitational backgrounds are discussed.

Abstract

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.