  We study nonequilibrium work relations for a space-dependent field with
stochastic dynamics (Model A). Jarzynski's equality is obtained through
symmetries of the dynamical action in the path integral representation. We
derive a set of exact identities that generalize the fluctuation-dissipation
relations to non-stationary and far-from-equilibrium situations. These
identities are prone to experimental verification. Furthermore, we show that a
well-studied invariance of the Langevin equation under supersymmetry, which is
known to be broken when the external potential is time-dependent, can be
partially restored by adding to the action a term which is precisely
Jarzynski's work. The work identities can then be retrieved as consequences of
the associated Ward-Takahashi identities.
