Finite renormalizations in the Epstein Glaser framework and renormalization of theS-matrix ofΦ4-theory

Pinter, G.

doi:10.1002/1521-3889(200104)10:4<333::aid-andp333>3.0.co;2-q

Cited by 24 publications

(33 citation statements)

References 8 publications

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“…This means that for (ϕ j , χ) = (ϕ l , ψ) the undetermined parameters (298) in ∆ F ϕ j ,χ and ∆ F ϕ l ,ψ have the same values. Note additionally ∆ F ϕ,χ = ±∆ F χ,ϕ due to (32).…”

Section: Normalization Of Time-ordered Products Of Symbols With Extermentioning

confidence: 99%

The Master Ward Identity

2002

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In the framework of perturbative quantum field theory (QFT) we propose a new, universal (re)normalization condition (called 'master Ward identity') which expresses the symmetries of the underlying classical theory. It implies for example the field equations, energy-momentum, chargeand ghost-number conservation, renormalized equal-time commutation relations and BRST-symmetry.It seems that the master Ward identity can nearly always be satisfied, the only exceptions we know are the usual anomalies. We prove the compatibility of the master Ward identity with the other (re)normalization conditions of causal perturbation theory, and for pure massive theories we show that the 'central solution' of Epstein and Glaser fulfills the master Ward identity, if the UV-scaling behavior of its individual terms is not relatively lowered.Application of the master Ward identity to the BRST-current of nonAbelian gauge theories generates an identity (called 'master BRST-identity') which contains the information which is needed for a local construction of the algebra of observables, i.e. the elimination of the unphysical fields and the construction of physical states in the presence of an adiabatically switched off interaction.

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Section: Normalization Of Time-ordered Products Of Symbols With Extermentioning

confidence: 99%

The Master Ward Identity

2002

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“…In particular, one obtains the diffeomorphism group on the space of coupling constants, tangent to the identity, which is nothing else than the renormalization group in the sense of Stückelberg and Petermann and was independently derived in form of the Main Theorem of Renormalization in [PS82,Pin01,DF04,BDF09]. Other structures refer to computational methods and can best be formulated in terms of Hopf algebras of graphs.…”

Section: Hopf Algebra and Renormalizationmentioning

confidence: 99%

“…The ambiguity is best described in terms of the Main Theorem of Renormalization [PS82,Pin01,DF04,BDF09]. Let the formal S-matrix be defined as the generating functional of time-ordered products, formally given by…”

Section: Functional Approach and Epstein-glaser Renormalizationmentioning

confidence: 99%

Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization

Dütsch¹,

Fredenhagen²,

Keller³

et al. 2014

Journal of Mathematical Physics

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We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. This closed expression, which we call the Epstein-Glaser Forest Formula, is analogous to Zimmermann's Forest Formula for BPH renormalization. For scalar fields the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.

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“…In causal perturbation theory this was termed Main Theorem of Renormalization [44]. Different versions of this theorem may be found in [46,22,3,44,38,25]. But there, in contrast to the formulation of renormalization in terms of the action functional, the parameters of a model are test functions.…”

Section: Main Theorem Of Perturbative Renormalizationmentioning

confidence: 99%

Causal Perturbation Theory in Terms of Retarded Products, and a Proof of the Action Ward Identity

2004

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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 [42]. 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 ' [45]. The theory depends on free parameters which flow under the renormalization group. This flow can be derived in our local * Work supported by the Deutsche Forschungsgemeinschaft.1 framework independently of the infrared behavior, as was first established by Hollands and Wald [32]. We explicitly compute non-trivial examples for the renormalization of the interaction and the field.

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Finite renormalizations in the Epstein Glaser framework and renormalization of theS-matrix ofΦ4-theory

Cited by 24 publications

References 8 publications

The Master Ward Identity

The Master Ward Identity

Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization

Causal Perturbation Theory in Terms of Retarded Products, and a Proof of the Action Ward Identity

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