Stuckelberg Petermann and

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Connection between the renormalization groups of Stuckelberg- Petermann and Wilson M. Dutsch Introduction Star-product quantization Stuckelberg - Petermann RG Regularized time-ordered product Flow of effective potential Comparism with usual flow equation formalism Conclusions Connection between the renormalization groups of Stuckelberg-Petermann and Wilson Michael Dutsch joint work with Romeo Brunetti and Klaus Fredenhagen Reference: Adv. Theor. Math. Phys. (to appear), math-ph/0901.2038 June 14, 2010

  • perturbation theory

  • stuckelberg - petermann rg

  • star-product quantization

  • regularized time-ordered

  • product

  • causal perturbation


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Connect groups
ion between the renormalization ofSt¨uckelberg-Petermannand Wilson
MichaelD¨utsch joint work with Romeo Brunetti and Klaus Fredenhagen Reference: Adv. Theor. Math. Phys. (to math-ph/0901.2038
June
14,
2010
appear),
Connection between the renormalization groups of St¨ckelberg-u Petermann and Wilson
M.D¨utsch
Introduction
Star-product quantization
Stu¨ckelberg-Petermann RG
Regularized time-ordered product
Flow of effective potential
Comparism with usual flow equation formalism
Conclusions
Outline
Introduction
Star-product quantization
St¨uckelberg-PetermannRG
Regularized time-ordered product
Flow of effective potential
Comparism with usual flow equation formalism
Conclusions
Different versions of RG, understood. This talk is restricted
their
relations
to perturbation
are
not
theory
completely
and
treats:
Connection between the renormalization groups of St¨uckelberg-Petermann and Wilson
M.Du¨tsch
Introduction
Star-product quantization
St¨uckelberg-Petermann RG
Regularized time-ordered product
Flow of effective potential
Comparism with usual flow equation formalism
Conclusions
Different versions of RG, their relations are not completely understood. This talk is restricted to perturbation theory and treats: tSeblekcu¨eret-PrgRGnnmaR(Causal perturbation theory) Non-uniqueness ofS-matrix.
Connection between the renormalization groups of St¨uckelberg-Petermann and Wilson
M.Du¨tsch
Introduction
Star-product quantization
St¨uckelberg-Petermann RG
Regularized time-ordered product
Flow of effective potential
Comparism with usual flow equation formalism
Conclusions
Different versions of RG, their relations are not completely understood. This talk is restricted to perturbation theory and treats: RGnnmaeretP-greblekcu¨tSR(Causal perturbation theory) Non-uniqueness ofS-matrix. ˆ ChangeSSof the renormalization presription can be absorbed in a renormalization of the interaction VZ(V):
ˆ S(V) =S(Z(V))
V
R={appearingZ}is a group - group of finite renormalizations ofS.
Connection between the renormalization groups of St¨uckelberg-Petermann and Wilson M.Du¨tsch
Introduction
Star-product quantization
St¨uckelberg-Petermann RG
Regularized time-ordered product
Flow of effective potential
Comparism with usual flow equation formalism
Conclusions
RG in the sense on a cutoff Λ.
of
Wilson:
dependence
of
the
theory
Connection between the renormalization groups of Stu¨ckelberg-Petermann and Wilson
M.D¨utsch
Introduction
Star-product quantization
Stu¨ckelberg-Petermann RG
Regularized time-ordered product
Flow of effective potential
Comparism with usual flow equation formalism
Conclusions
RG in the on a cutoff
sense Λ.
of
Wilson:
dependence
In terms of regularized Feynman defines regularizedS-matrixSΛ.
of
propagator
the
pΛ
theory
one
Connection between the renormalization groups of St¨uckelberg-Petermann and Wilson
M.Du¨tsch
Introduction
Star-product quantization
Stu¨ckelberg-Petermann RG
Regularized time-ordered product
Flow of effective potential
Comparism with usual flow equation formalism
Conclusions
RG in the sense on a cutoff Λ.
of
Wilson:
dependence
of the
In terms of regularized Feynman propagatorpΛ defines regularizedS-matrixSΛ.
t
Definition of the effective potentialVΛa V Thenoriginal interaction. SΛ(VΛ) =S(V) i.e.VΛ:=SΛ1S(V)
scale
theory
one
Λ:
Let
Connection between the renormalization groups of Stu¨ckelberg-Petermann and Wilson
M. Dutsch ¨
Introduction
Star-product quantization
Stu¨ckelberg-Petermann RG
Regularized time-ordered product
Flow of effective potential
Comparism with usual flow equation formalism
Conclusions