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

Kazakov, D.I.

doi:10.1016/0370-2693(83)90816-X

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

D.I. Kazakov
(
- Dubna, JINR
)

1983

5 pages

Published in:

Phys.Lett.B 133 (1983) 406-410

Published: 1983

DOI:

10.1016/0370-2693(83)90816-X

View in:

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Citations per year

Abstract: (Elsevier)

We present a new method for multiloop calculations that provides an “algebraic” procedure to evaluate the renormalization group functions up to five loops. As an example, a final analytical expression for the five-loop β -function in the ϕ 4 theory is given.

FIELD THEORY: MASSLESS
MASSLESS: FIELD THEORY
FEYNMAN GRAPH: HIGHER-ORDER
RENORMALIZATION: BETA FUNCTION
field theory: scalar
NUMERICAL CALCULATIONS

References(6)

Figures(0)

[1]

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

[2]

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

[3]

preprint

D.I. Kazakov

[4]

Five Loop Renormalization Group Calculations in the $g \phi^4$ in Four-dimensions Theory

- Phys.Lett.B 132 (1983) 351
•
DOI:
- 10.1016/0370-2693(83)90324-6

[5]

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

[6]

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

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

Citations per year

1/NNN Expansion: Calculation of the Exponents η\etaη and Nu in the Order 1/N2N^2N2 for Arbitrary Number of Dimensions

CALCULATION OF MANY LOOP DIAGRAMS OF PERTURBATION THEORY

Five Loop Renormalization Group Calculations in the gϕ4g \phi^4gϕ4 in Four-dimensions Theory

Integration by parts: The algorithm to calculate β\betaβ-functions in 4 loops

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

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

Five Loop Renormalization Group Calculations in the $g \phi^4$ in Four-dimensions Theory

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