The Gaussian effective potential and stochastic partial differential equations

We investigate arbitrary stochastic partial differential equations subject to translation invariant and temporally white noise correlations from a nonperturbative framework. The method that we expose first casts the stochastic equations into a functional integral form, then it makes use of the Gaussian effective potential approach, which is an useful tool for describing symmetry breaking. We apply this method to the Kardar-Parisi-Zhang equation and find that the system exhibits spontaneous symmetry breaking in (1+1),(2+1) and (3+1) Euclidean dimensions, providing insight into the evolution of the system configuration due to the presence of noise correlations. A simple and systematic approach to the renormalization, without explicit regularization, is employed.