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Dimensional regularization
About: Dimensional regularization is a research topic. Over the lifetime, 1668 publications have been published within this topic receiving 63654 citations. The topic is also known as: DR.
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TL;DR: In this article, a new regularization and renormalization procedure for gauge theories is presented, which is particularly well suited for the treatment of gauge theories and is transparent when anomalies such as the Bell-Jackiw-Adler anomaly may occur.
3,722 citations
TL;DR: In this article, two program packages for evaluating one-loop amplitudes are presented, which can work either in dimensional regularization or in constrained differential renormalization, and they are shown to be equivalent to regularization by dimensional reduction.
1,564 citations
TL;DR: In this article, a generalized zeta function was proposed to regularize quadratic path integrals on a curved background spacetime, which can be expressed as a Mellin transform of the kernel of the heat equation which describes diffusion over the four dimensional spacetime manifold in a fith dimension of parameter time.
Abstract: This paper describes a technique for regularizing quadratic path integrals on a curved background spacetime. One forms a generalized zeta function from the eigenvalues of the differential operator that appears in the action integral. The zeta function is a meromorphic function and its gradient at the origin is defined to be the determinant of the operator. This technique agrees with dimensional regularization where one generalises ton dimensions by adding extra flat dimensions. The generalized zeta function can be expressed as a Mellin transform of the kernel of the heat equation which describes diffusion over the four dimensional spacetime manifold in a fith dimension of parameter time. Using the asymptotic expansion for the heat kernel, one can deduce the behaviour of the path integral under scale transformations of the background metric. This suggests that there may be a natural cut off in the integral over all black hole background metrics. By functionally differentiating the path integral one obtains an energy momentum tensor which is finite even on the horizon of a black hole. This energy momentum tensor has an anomalous trace.
1,251 citations
TL;DR: In this article, two program packages for evaluating one-loop amplitudes are presented, which can work either in dimensional regularization or in constrained differential renormalization, and they are shown to be equivalent to regularization by dimensional reduction.
Abstract: Two program packages are presented for evaluating one-loop amplitudes. They can work either in dimensional regularization or in constrained differential renormalization. The latter method is found at the one-loop level to be equivalent to regularization by dimensional reduction.
1,197 citations
TL;DR: In this article, the authors describe how to compute planar gluon scattering amplitudes at strong coupling in = 4 super Yang Mills by using the gauge/string duality, and find agreement with a recent ansatz by Bern, Dixon and Smirnov.
Abstract: We describe how to compute planar gluon scattering amplitudes at strong coupling in = 4 super Yang Mills by using the gauge/string duality. The computation boils down to finding a certain classical string configuration whose boundary conditions are determined by the gluon momenta. The results are infrared divergent. We introduce the gravity version of dimensional regularization to define finite quantities. The leading and subleading IR divergencies are characterized by two functions of the coupling that we compute at strong coupling. We compute also the full finite form for the four point amplitude and we find agreement with a recent ansatz by Bern, Dixon and Smirnov.
1,184 citations