Massless two-loop self-energy diagram: Historical review

Grozin, A.G.

doi:10.1142/S0217751X12300189

Massless two-loop self-energy diagram: Historical review

A.G. Grozin
(
- Novosibirsk, IYF
)

Jun, 2012

19 pages

Published in:

Int.J.Mod.Phys.A 27 (2012) 1230018

e-Print:

1206.2572 [hep-ph]

DOI:

10.1142/S0217751X12300189

Report number:

TTP12-019

View in:

pdf

reference search31 citations

Citations per year

Abstract: (arXiv)

This class of diagrams has numerous applications. Many interesting results have been obtained for it.

Note:

Extended version of the talk at the conference Advances of quantum field theory, Dubna, October 2011/ 19 pages. V2: 2 references added. V3: 2 references added

Multiloop Feynman diagrams
propagator: massless
review
history
radiative correction
higher-order: 2
master integral

References(32)

Figures(27)

[1]

Integration by parts: The algorithm to calculate $\beta$ -functions in 4 loops

K.G. Chetyrkin
(
- Moscow, INR
)
,
F.V. Tkachov
(
- Moscow, INR
)

- Nucl.Phys.B 192 (1981) 159-204,
- Nucl. Phys. B192 ( 1981) 159-204
•
DOI:
- 10.1016/0550-3213(81)90199-1

[1]

F.V. Tkachov

[1]

A theorem on analytical calculability of 4-loop renormalization group functions

F.V. Tkachov
(
- Moscow, INR
)

- Phys.Lett.B 100 (1981) 65-68
•
DOI:
- 10.1016/0370-2693(81)90288-4

[2]

Four Loop Massless Propagators: An Algebraic Evaluation of All Master Integrals

P.A. Baikov
(
- SINP, Moscow
)
,
K.G. Chetyrkin
(
- KIT, Karlsruhe, TTP and
- Moscow, INR
)

- Nucl.Phys.B 837 (2010) 186-220
•
e-Print:
- 1004.1153
•
DOI:
- 10.1016/j.nuclphysb.2010.05.004

[3]

New Approach to Evaluation of Multiloop Feynman Integrals: The Gegenbauer Polynomial x Space Technique

- Nucl.Phys.B 174 (1980) 345-377
•
DOI:
- 10.1016/0550-3213(80)90289-8

[4]

1/ $N$ Expansion: Calculation of the Exponents $\eta$ and Nu in the Order 1/ $N^2$ for Arbitrary Number of Dimensions

- Theor.Math.Phys. 47 (1981) 465-475,
- Teor.Mat.Fiz. 47 (1981) 291-306,
- Teor. Mat. Fiz. 47 ( 1981) 291-306
•
DOI:
- 10.1007/BF01019296

[5]

CALCULATION OF MANY LOOP DIAGRAMS OF PERTURBATION THEORY

N.I. Usyukina
(
- Moscow State U.
)

- Theor.Math.Phys. 54 (1983) 78-81,
- Teor.Mat.Fiz. 54 (1983) 124-129
•
DOI:
- 10.1007/BF01017127

[6]

CALCULATION OF FEYNMAN INTEGRALS BY THE METHOD OF 'UNIQUENESS'

D.I. Kazakov
(
- Dubna, JINR
)

- Theor.Math.Phys. 58 (1984) 223-230,
- Teor.Mat.Fiz. 58 (1984) 343-353
•
DOI:
- 10.1007/BF01018044

[6]

THE METHOD OF UNIQUENESS, A NEW POWERFUL TECHNIQUE FOR MULTILOOP CALCULATIONS

D.I. Kazakov
(
- Dubna, JINR
)

- Phys.Lett.B 133 (1983) 406-410
•
DOI:
- 10.1016/0370-2693(83)90816-X

[7]

Multiloop Calculations: Method of Uniqueness and Functional Equations

D.I. Kazakov
(
- Dubna, JINR
)

- Theor.Math.Phys. 62 (1985) 84-89,
- Teor.Mat.Fiz. 62 (1984) 127-135
•
DOI:
- 10.1007/BF01034829

[8]

Quantum field renormalization group in the theory of critical behavior and stochastic dynamics, Sankt Petersburg (1998), Chap. 4, Sect. 36

A.N. Vasiliev

[9]

Trace Anomalies and $\lambda \phi^4$ Theory in Curved Space

S.J. Hathrell
(
- Cambridge U.
)

- Annals Phys. 139 (1982) 136
•
DOI:
- 10.1016/0003-4916(82)90008-2

[9]

Trace Anomalies and {QED} in Curved Space

S.J. Hathrell
(
- Cambridge U.
)

- Annals Phys. 142 (1982) 34
•
DOI:
- 10.1016/0003-4916(82)90227-5

[10]

TMΦ 58 (1984) 343

S.G. Gorishnii
,
A.P. Isaev

- Theor.Math.Phys. 58 (1984) 232

[11]

Exploiting the 1.440 Fold Symmetry of the Master Two Loop Diagram

David J. Broadhurst
(
- Open U., England
)

- Z.Phys.C 32 (1986) 249-253,
- Z. Phys. C32 ( 1986) 249-253
•
DOI:
- 10.1007/BF01552503

[12]

$Z$ (2) X S(6) Symmetry of the Two Loop Diagram

- Z.Phys.C 41 (1988) 81
•
DOI:
- 10.1007/BF01412581

[13]

The Gegenbauer polynomial technique: The Evaluation of a class of Feynman diagrams

A.V. Kotikov
(
- Annecy, LAPP
)

- Phys.Lett.B 375 (1996) 240-248
•
e-Print:
- hep-ph/9512270
•
DOI:
- 10.1016/0370-2693(96)00226-2

[14]

Beyond the triangle and uniqueness relations: Nonzeta counterterms at large N from positive knots

David J. Broadhurst
(
- Open U., England
)
,
J.A. Gracey
(
- Liverpool U.
)
,
D. Kreimer
(
- Mainz U., Inst. Phys.
)

- Z.Phys.C 75 (1997) 559-574
•
e-Print:
- hep-th/9607174
•
DOI:
- 10.1007/s002880050500

[15]

Nested sums, expansion of transcendental functions and multiscale multiloop integrals

Sven Moch
(
- Karlsruhe U., TTP
)
,
Peter Uwer
(
- Karlsruhe U., TTP
)
,
Stefan Weinzierl
(
- Parma U. and
- INFN, Parma
)

- J.Math.Phys. 43 (2002) 3363-3386
•
e-Print:
- hep-ph/0110083
•
DOI:
- 10.1063/1.1471366

[16]

Where do the tedious products of zeta's come from?

David J. Broadhurst
(
- Open U., England
)

- Nucl.Phys.B Proc.Suppl. 116 (2003) 432-436,
•
e-Print:
- hep-ph/0211194
•
DOI:
- 10.1016/S0920-5632(03)80214-1

[17]

M. Pismak, Yu

S.E. Derkachev
,
J. Honkonen

- J.Phys.A 23 (1990) 5563

[18]

On calculation of (2+epsilon) RG functions in the Gross-Neveu model from large N expansions of critical exponents

N.A. Kivel
(
- St. Petersburg, INP
)
,
A.S. Stepanenko
(
- St. Petersburg, INP
)
,
A.N. Vasiliev
(
- St. Petersburg State U.
)

- Nucl.Phys.B 424 (1994) 619-627
•
e-Print:
- hep-th/9308073
•
DOI:
- 10.1016/0550-3213(94)90411-1

[19]

A Method of evaluating massive Feynman integrals

E.E. Boos
(
- Moscow State U.
)
,
Andrei I. Davydychev
(
- Moscow State U.
)

- Theor.Math.Phys. 89 (1991) 1052-1063,
- Teor.Mat.Fiz. 89 (1991) 56-72
•
DOI:
- 10.1007/BF01016805

[20]

TMΦ 22 (1975) 300

N.I. Usyukina

- Theor.Math.Phys. 22 (1975) 210

[21]

The Massless two loop two point function

Isabella Bierenbaum
(
- Mainz U., Inst. Phys.
)
,
Stefan Weinzierl
(
- Parma U. and
- INFN, Parma
)

- Eur.Phys.J.C 32 (2003) 67-78
•
e-Print:
- hep-ph/0308311
•
DOI:
- 10.1140/epjc/s2003-01389-7

1-25 of 32
1
2
25 / page