Axiomatic quantum field theory. Jet formalism

TL;DR

This paper explores an axiomatic approach to quantum field theory using jet formalism, establishing a connection between classical symmetries and quantum Green functions within a graded algebra framework.

Contribution

It introduces a formulation of QFT compatible with jet formalism, linking classical variational symmetries to quantum Green function identities via graded algebra homomorphisms.

Findings

Classical variational symmetries lead to identities for Euclidean Green functions.

The algebra of Euclidean quantum fields is graded commutative.

Homomorphisms connect classical fields to quantum field algebras.

Abstract

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.