From path integral quantization to stochastic quantization: a pedestrian's journey.

This paper presents two novel proofs demonstrating the equivalence between path integral quantization and stochastic quantizations for generic scalar Euclidean quantum field theories. The proofs utilize Taylor interpolations indexed by forests, inspired by constructive field theory, operating both at the level of individual Feynman expansion terms and directly at the path integral level. This work provides fundamental insights into quantum field theory.