A path integral equivalent to a Langevin equation can be obtained from the corresponding Fokker–Planck equation or by transforming the Gaussian probability distribution P ( η η ) ( η η ) d η η of the fluctuating force η η to a probability distribution of the slow variables, schematically P ( A ) d A = P ( η η ) ( η η ( A ) ) det ( d η η / d A ) d A . The functional determinant and associated mathematical subtleties drop out if the Langevin equation is discretized in the natural (causal) way, where A ( t + Δ Δ t ) − − A ( t ) depends on A ( t ) but not on A ( t + Δ Δ t ) . It turns out to be convenient to introduce auxiliary response variables A ~ ~ . The path integral equivalent to the generic Langevin equation then reads ∫ ∫ P ( A , A ~ ~ ) d A d A ~ ~ = N ∫ ∫ exp ⁡ ⁡ ( L ( A , A ~ ~ ) ) d A d A ~ ~ , where N is a normalization factor and L ( A , A ~ ~ ) = ∫ ∫ ∑ ∑ i , j { A ~ ~ i λ λ i , j A ~ ~ j − − A ~ ~ i { δ δ i , j d A j d t − − k B T [ A i , A j ] d H d A j + λ λ i , j d H d A j − − d λ λ i , j d A j } } d t . The path integral formulation allows for the use of tools from quantum field theory, such as perturbation and renormalization group methods. This formulation is typically referred to as either the Martin-Siggia-Rose formalism or the Janssen-De Dominicis formalism after its developers. The mathematical formalism for this representation can be developed on abstract Wiener space.