Diffeomorphism symmetry in φ4 field theory

The diffeomorphism and Weyl transformations in the renormalized D-dimensional φ4 theory are considered. The action functional including the sources of the operators φ2 and φ4 appears to be invariant with respect to these transformations with the appropriate choice of their form for the field and sources. For the generalized diffeomorphism transformation being some combination of diffeomorphism and Weyl transformations, the Ward identities for the renormalized Green functions of the field φ and operators φ2, φ4 are obtained. In the critical point they are similar to the Ward identities used in the 2D conformal field theory and enable one to prove the conformal invariance of φ2 and φ4 for arbitrary dimension D. (author)