AbstractBy generalizing the integration by parts formula on the function space, the isomorphism between the general class of selfinteracting Euclidean, Bose fields and classical gases is proven in a nonperturbative way. Rigorous, non‐perturbative derivations of the Mayer equations and Bogoliubov‐Born‐Kirkwood‐Grenn‐Yvone hierarchical equations are given. Expansions of several physical quantities are discussed in terms of the linear graphs, for some general classes of Euclide