Free fields in any dimensions are well-known to be Gaussian, act on the Fock space and satisfy the canonical commutation relations.
By definition, interacting field operators are NOT such cases, as seen in the $\phi^4_3$ theory.
However, I vaguely remember seeing in some paper that in $2$ dimensional Euclidean space (or $1+1$ dimensional Minkowski spacetime), interacting fields do satisfy the canonical commutation relations and their co-located products are just Wick products and so on...
I tried to search for relevant resources, but cannot find an explicit statement & proof of these issues.
Could anyone please clarify for me or provide some references?
