  There is recent interest in finding a potential formulation for Stochastic
Partial Differential Equations (SPDEs). The rationale behind this idea lies in
obtaining all the dynamical information of the system under study from one
single expression. In this Letter we formally provide a general Lagrangian
formalism for SPDEs using the Hojman et al. method. We show that it is possible
to write the corresponding effective potential starting from an s-equivalent
Lagrangean, and that this potential is able to reproduce all the dynamics of
the system, once a special differential operator has been applied. This
procedure can be used to study the complete time evolution and spatial
inhomogeneities of the system under consideration, and is also suitable for the
statistical mechanics description of the problem. Keywords: stochastic partial
differential equations, variational formulation, effective potential. PACS:
45.20.Jj; 02.50.-r; 02.50.Ey.
