  By generalizing the quantum weak measurement protocol to the case of quantum
fields, we show that weak measurements probe an effective classical background
field that describes the average field configuration in the spacetime region
between pre- and post-selection boundary conditions. The classical field is
itself a weak value of the corresponding quantum field operator and satisfies
equations of motion that extremize an effective action. Weak measurements
perturb this effective action, producing measurable changes to the classical
field dynamics. As such, weakly measured effects always correspond to an
effective classical field. This general result explains why these effects
appear to be robust for pre- and post-selected ensembles, and why they can also
be measured using classical field techniques that are not weak for individual
excitations of the field.
