Action Ward Identity and the Stückelberg-Petermann Renormalization Group

Dütsch, Michael; Fredenhagen, Klaus

doi:10.1007/978-3-7643-7434-1_9

Cited by 14 publications

(14 citation statements)

References 20 publications

(24 reference statements)

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“…The presence of derivative couplings introduces an additional freedom in the choice of the extension in each step of the EpsteinGlaser induction and one has to use it to fulfill (88). This relation follows basically from the Action Ward Identity, as discussed in [21,20]. It can be also seen as a consistency condition implementing the Leibniz rule, see [34].…”

Section: Example 73 (Removing Tadpoles)mentioning

confidence: 92%

Perturbative Algebraic Quantum Field Theory

Rejzner¹

2016

Mathematical Physics Studies

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Section: Example 73 (Removing Tadpoles)mentioning

confidence: 92%

Perturbative Algebraic Quantum Field Theory

Rejzner¹

2016

Mathematical Physics Studies

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“…A first answer to this latter question was already given in [27] (for a more explicit formulation in Minkowski space see [16,17]), and an elaboration on this approach was the starting point of the present work.…”

Section: Motivations and Planmentioning

confidence: 98%

Perturbative algebraic quantum field theory and the renormalization groups

Brunetti¹,

Dütsch²,

Fredenhagen³

2009

Advances in Theoretical and Mathematical Physics

128

327

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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 Stückelberg-Petermann renormalization group which describes the freedom in the perturbative construction with e-print archive: http://lanl.arXiv.org/abs/hep-th//0901.2038 R. BRUNETTI ET AL.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 one-parametric subfamily of the Stückelberg-Petermann group and that this subfamily is in general only a cocycle. Since the algebraic structure of the Stückelberg-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 β-function in a state independent way.

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“…This representation of local functionals as smeared fields can be made unique by introducing the subspace of balanced fields P bal ⊂ P [16,20]:…”

Section: Classical Field Theory For Localized Interactionsmentioning

confidence: 99%

“…By introducing the differential operator 20) we obtain from (2.12) the following explicit expression for the interacting field:…”

Section: )mentioning

confidence: 99%

Removal of Violations of the Master Ward Identity in Perturbative QFT

2008

Self Cite

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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 , 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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Action Ward Identity and the Stückelberg-Petermann Renormalization Group

Cited by 14 publications

References 20 publications

Perturbative Algebraic Quantum Field Theory

Perturbative Algebraic Quantum Field Theory

Perturbative algebraic quantum field theory and the renormalization groups

Removal of Violations of the Master Ward Identity in Perturbative QFT

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