Calculation of Feynman diagrams by the ?Uniqueness? method

Kazakov, D. I.

doi:10.1007/bf01018044

Cited by 106 publications

(129 citation statements)

References 8 publications

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“…(2). were evaluated long ago [19,20]. As an additional cross check, the integral reduction and evaluation is also performed using the program MINCER [21,22].…”

Section: A Methodsmentioning

confidence: 99%

Regularization schemes and higher order corrections

Kilgore

2011

Phys. Rev. D

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[kilgore@bnl.gov] I apply commonly used regularization schemes to a multi-loop calculation to examine the properties of the schemes at higher orders. I find complete consistency between the conventional dimensional regularization scheme and dimensional reduction, but I find that the four dimensional helicity scheme produces incorrect results at next-to-next-to-leading order and singular results at next-tonext-to-next-to-leading order. It is not, therefore, a unitary regularization scheme.

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“…(2). were evaluated long ago [19,20]. As an additional cross check, the integral reduction and evaluation is also performed using the program MINCER [21,22].…”

Section: A Methodsmentioning

confidence: 99%

Regularization schemes and higher order corrections

Kilgore

2011

Phys. Rev. D

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“…The method [3,9] consists of the combined application of several characteristic identities to diagrams with certain ideal line index constellations. To reach such constellations, the indices are manipulated, after a Fourier transformation, by a configuration space version of the triangle rule of the last section, or by the insertion of a φ 2 -vertex.…”

Section: Methods Of Ideal Index Constellations In Configuration Spacementioning

confidence: 99%

“…(13.71) solves the integral if three elements (lines, vertices or triangles) are one step from an ideal index constellation [9,3]. : ideal one step from ideal simple lines line…”

Section: Transformation Of Indicesmentioning

confidence: 99%

Calculation of Momentum Space Integrals

Kleinert¹,

Schulte-Frohlinde²

2001

Critical Properties of Phi⁴-Theories

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“…9 with n i → d 2 − n i . There is an additional symmetry following from the star-triangle relation [4,5]. The 5-th basis integral is proportional to the 2-loop diagram G (1, 1, 1, 1, n) with a noninteger index of the middle line n = ε, and will be discussed in Sect.…”

Section: Loopsmentioning

confidence: 99%

“…3, and massive on-shell diagrams -in Sect. 4. Finally, some mathematical methods, most useful in massless and HQET calculations, are considered in Sect.…”

Section: Introductionmentioning

confidence: 99%

Lectures on Multiloop Calculations

Grozin

2004

Int. J. Mod. Phys. A

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I discuss methods of calculation of propagator diagrams (massless, those of Heavy Quark Effective Theory, and massive on-shell diagrams) up to 3 loops. Integrationby-parts recurrence relations are used to reduce them to linear combinations of basis integrals. Non-trivial basis integrals have to be calculated by some other method, e.g., using Gegenbauer polynomial technique. Many of them are expressed via hypergeometric functions; in the massless and HQET cases, their indices tend to integers at ε → 0. I discuss the algorithm of their expansion in ε, in terms of multiple ζ values. These lectures were given at Calc-03 school, Dubna, 14-20 June 2003.

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Calculation of Feynman diagrams by the ?Uniqueness? method

Cited by 106 publications

References 8 publications

Regularization schemes and higher order corrections

Regularization schemes and higher order corrections

Calculation of Momentum Space Integrals

Lectures on Multiloop Calculations

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