A set of Green functions Gα(x − y), α ∈ [0, 2π[, for free scalar field theory is introduced, varying between the Hadamard Green function ∆1(x − y) ≡ 〈0 | {φ(x), φ(y)} | 0〉 and the causal Green function Gπ(x − y) = i∆(x − y) ≡ [φ(x), φ(y)]. For every α ∈ [0, 2π[ a path-integral representation for Gα is obtained both in the configuration space and in the phase space of the classical relativistic ...