  Jet formalism provides the adequate mathematical formulation of classical
field theory, reviewed in hep-th/0612182v1. A formulation of QFT compatible
with this classical one is discussed. We are based on the fact that an algebra
of Euclidean quantum fields is graded commutative, and there are homomorphisms
of the graded commutative algebra of classical fields to this algebra. As a
result, any variational symmetry of a classical Lagrangian yields the
identities which Euclidean Green functions of quantum fields satisfy.
