Stuckelberg Petermann and

Michael Dutsch

Description

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

Sujets

• Brunetti
• Perturbation theory
• Product

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 27
• Langue: English

Extrait

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 ChangeS→Sof the renormalization presription can be absorbed in a renormalization of the interaction V→Z(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-matrixS Λ .

of

propagator

the

p Λ

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 propagatorp Λ defines regularizedS-matrixS Λ .

t

Definition of the effective potentialV Λ a V Thenoriginal interaction. S Λ (V Λ ) =S(V) i.e.V Λ :=S Λ −1 ◦S(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