Jet formalism provides the
adequate mathematical formulation of classical field theory, reviewed in hep-th/0612182. 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.
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