  We introduce the functional field integral approach to study the statistics
of quantum work under nonequilibrium conditions and derive the general
formalism for a bilinear Hamiltonian with arbitrary time dependence. The method
is then examined in three models. For the transverse Ising chain, it yields the
correct quantum critical scaling and dynamical quantum phase transitions for
single and double quench protocols, respectively. For the Su-Schrieffer-Heeger
(SSH) model, we observe nonuniversal quantum critical scaling with anomalous
$1/N$-correction due to its topological nature. Dynamical quantum phase
transitions are observed for three different time evolution protocols but their
time periodicity only appears in the double quench case. We then extend our
method to the Bardeen-Cooper-Schrieffer (BCS) model for superconductivity and
discuss the possibility of its application for general correlated models in
combination with either the mean-field approximation or exact Monte Carlo
simulations on classical (auxiliary) fields or disorders. Our method has the
advantage of numerical simplicity, in the cost of explicit state evolution, and
provides a promising way for exploring the physics of quantum work under
general conditions.
