Perturbative Algebraic Quantum Field Theory and the Renormalization Groups
By R. Brunetti, M. Duetsch, K. Fredenhagen. 2009
189 citations recorded by the source corpus.
A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low dimensional theories and of non-polynomial interactions. We discuss the connection between the Stueckelberg-Petermann renormalization group which describes the freedom in the perturbative construction with the Wilsonian idea of theories at different scales . In particular we relate the approach to renormalization in terms of Polchinski's Flow Equation to the Epstein-Glaser method. We also show that the renormalization group in the sense of Gell-Mann-Low (which characterizes the behaviour of the theory under the change of all scales) is a 1-parametric subfamily of the Stueckelberg-Petermann group and that this subfamily is in general only a cocycle. Since the algebraic structure of the Stueckelberg-Petermann group does not depend on global quantities, this group can be formulated in the (algebraic) adiabatic limit without meeting any infrared divergencies. In particular we derive an algebraic version of the Callan-Symanzik equation and define the beta-function in a state independent way.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/149746db2241f86e4a0bdac81474f825af3323c9
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Batalin-Vilkovisky Formalism in Perturbative Algebraic Quantum Field Theory (2011, methodology): “A question left open in [20] was whether also the renormalized time ordered product can be extended to a binary product on a suitable space of functionals.”