  We study the work cost of processes in quantum fields without the need of
projective measurements, which are always ill defined in quantum field theory.
Inspired by interferometry schemes, we propose a work distribution that
generalizes the two-point measurement scheme employed in quantum thermodynamics
to the case of quantum fields and avoids the use of projective measurements.
The distribution is calculated for local unitary processes performed on
Kubo-Martin-Schwinger (thermal) states of scalar fields. Crooks theorem and the
Jarzynski equality are shown to be satisfied for a family of spatio-temporally
localized unitaries, and some features of the resulting distributions are
studied as functions of temperature and the degree of localization of the
unitary operation. We show how the work fluctuations become much larger than
the average as the process becomes more localized in both time and space.
