2007

Removal of violations of the Master Ward Identity in perturbative QFT

Brennecke, Ferdinand, Duetsch, Michael

Understand

We study the appearance of anomalies of the Master Ward Identity, which is a universal renormalization condition in perturbative QFT.

The main insight of the present paper is that any violation of the Master Ward Identity can be expressed as a LOCAL interacting field; this is a version of the well-known Quantum Action Principle of Lowenstein and Lam.
Proceeding in a proper field formalism by induction on the order in $\hbar$, this knowledge about the structure of possible anomalies as well as techniques of algebraic renormalization are used to remove possible anomalies by finite renormalizations.
As an example the method is applied to prove the Ward identities of the O(N) scalar field model.

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Then

“Perturbative algebraic field theory, and deformation quantization”
Dütsch, M. and Fredenhagen, K · 2001
Later among the works it cites.
“Algebraic quantum field theory, perturbation theory, and the loop expansion”
Dütsch, M. and Fredenhagen, K · 2001
Later among the works it cites.
“The Master Ward identity”
Dütsch, M. and Boas, F. M · 2002
Later among the works it cites.
“The Master Ward identity and generalized Schwinger-Dyson equation in classical field theory”
Dütsch, M. and Fredenhagen, K · 2003
Later among the works it cites.
“Causal perturbation theory in terms of retarded products, and a proof of the Action Ward identity”
Dütsch, M. and Fredenhagen, K · 2004
Later among the works it cites.
“Proof of perturbative gauge invariance for tree diagrams to all orders”
Dütsch, M · 2005
Later among the works it cites.
“Conservation of the stress tensor in interacting quantum field theory in curved spacetimes”
Hollands, S. and Wald, R. M · 2005
Later among the works it cites.
“Investigations to the anomaly problem of the Master Ward Identity”
Brennecke, F · 2005
Later among the works it cites.
“Action Ward identity and the Stückelberg-Petermann renormalization group”
Dütsch, M. and Fredenhagen, K · 2006
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“Renormalized Quantum Yang-Mills Fields in Curved Spacetime” (2007)
Hollands, S · 2007
Closest in time.

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