In QFT there are two very useful general approaches to study quantum fields (on the Minkowski space-time): path integrals and operator formalism. Sometimes they give the same results, sometimes one formalism is better than another.
My question is what happens in the Euclidean space-time (e.g. statistical physics)? As far as I know the formalism of path integrals is widely used in the field, but what about the operator formalism? In particular I would be happy to have a reference to a detailed discussion of the free scalar field in Euclidean space time in dimension greater than 2 (the 2d massless case is discussed in several books on CFT).