  Classical field theories coupled to stochastic noise provide an extremely
powerful tool for modeling phenomena as diverse as turbulence,
pattern-formation, and the structural development of the universe itself. In
this Letter we sketch a general formalism that maps such systems into a field
theory language, and demonstrate how to extract the one-loop physics for an
arbitrary classical field theory coupled to Gaussian noise. The amplitude of
the noise two-point function serves as the loop-counting parameter and is the
analog of Planck's constant hbar in quantum field theory. We define the
effective action and the effective potential, and derive a general formula for
the one-loop effective potential of a classical field theory coupled to
translation-invariant Gaussian noise.
