In this talk I’ll introduce time-sliced perturbation theory (TSPT) a method to study the mildly non-linear regime of large scale structure. TSPT concentrates in the evolution of the probability distribution function for cosmological fields, which has certain advantages with respect to the standard approach. I will describe two of them: first, the approach automatically incorporates Galilean invariance. This allows for a systematic treatment of the non-linear evolution of the BAO. Second, it allows a path integral formulation of the problem of structure formation which treats the problems related to the UV sensitivity in a language closer to other field theories. The latter has an impact on the parameterisation of the UV sensitivity of the bispectrum.