Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity

Details Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity

2004-03-22

arxiv.org/abs/hep-th/0403213v3

Physics

High Energy Physics

High Energy Physics - Theory

76 pages, to appear in Rev. Math. Phys

Scientific paper

10.1142/S0129055X04002266

In the framework of perturbative algebraic quantum field theory a local construction of interacting fields in terms of retarded products is performed, based on earlier work of Steinmann. In our formalism the entries of the retarded products are local functionals of the off shell classical fields, and we prove that the interacting fields depend only on the action and not on terms in the Lagrangian which are total derivatives, thus providing a proof of Stora's 'Action Ward Identity'. The theory depends on free parameters which flow under the renormalization group. This flow can be derived in our local framework independently of the infrared behavior, as was first established by Hollands and Wald. We explicitly compute non-trivial examples for the renormalization of the interaction and the field.

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