Negative dimensional integrals. I. Feynman graphs

Halliday, I.G.; Ricotta, Regina Maria

doi:10.1016/0370-2693(87)91229-9

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Cited by 73 publications

(51 citation statements)

References 6 publications

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“…Ricotta and G.V. Dunne [10,11,17]. The work involves an analytic extension of D to negative values, so the method was labeled NDIM (negative dimensional integration method).…”

Section: Introductionmentioning

confidence: 99%

Definite integrals by the method of brackets. Part 1☆☆The first author was partially funded by Fondecyt (Chile), Grant number 3080029. The work of the second author was partially funded by NSF-DMS 0070567.

González

Moll

2010

Advances in Applied Mathematics

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“…Ricotta and G.V. Dunne [10,11,17]. The work involves an analytic extension of D to negative values, so the method was labeled NDIM (negative dimensional integration method).…”

Section: Introductionmentioning

confidence: 99%

Definite integrals by the method of brackets. Part 1☆☆The first author was partially funded by Fondecyt (Chile), Grant number 3080029. The work of the second author was partially funded by NSF-DMS 0070567.

González

Moll

2010

Advances in Applied Mathematics

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“…The aim of this work is to present an improved and more general technique related with NDIM (Negative Dimensional Integration Method) , [ 1], [ 2], [ 3], [ 4], [ 5], [ 6], which we have called Method of Brackets. This modification to NDIM was originally presented in [ 7] in the context of multiloops Feynman integrals.…”

Section: Introductionmentioning

confidence: 99%

Method of Brackets and Feynman diagram evaluation

González

2010

Nuclear Physics B - Proceedings Supplements

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“…Another integration method that has been developed in recent years and applied with great success is the negative dimensional integration method (NDIM) [15]. This method uses the analytic continuation of dimension D into negative values.…”

Section: Introductionmentioning

confidence: 99%

Massless and massive one-loop three-point functions in negative dimensional approach

2002

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In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time D. Our approach reproduces the known results as well as other solutions as yet unknown in the literature. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories.

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Negative dimensional integrals. I. Feynman graphs

Cited by 73 publications

References 6 publications

Definite integrals by the method of brackets. Part 1☆☆The first author was partially funded by Fondecyt (Chile), Grant number 3080029. The work of the second author was partially funded by NSF-DMS 0070567.

Definite integrals by the method of brackets. Part 1☆☆The first author was partially funded by Fondecyt (Chile), Grant number 3080029. The work of the second author was partially funded by NSF-DMS 0070567.

Method of Brackets and Feynman diagram evaluation

Massless and massive one-loop three-point functions in negative dimensional approach

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