Dimensional renormalization and the action principle

Breitenlohner, P.; Maison, Dieter

doi:10.1007/bf01609069

Cited by 717 publications

(836 citation statements)

References 12 publications

(18 reference statements)

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“…As before in Refs. [11,14,15,20] we employ the so-called Larin scheme [11,26] which, at the present level, is equivalent to, but computationally more convenient than the original prescription [27,28] for consistently dealing with γ 5 in dimensional regularization. See also the discussion in Ref.…”

Section: Formalism and Calculationmentioning

confidence: 99%

Third-order QCD corrections to the charged-current structure function

2009

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We compute the coefficient function for the charge-averaged W ± -exchange structure function F 3 in deep-inelastic scattering (DIS) to the third order in massless perturbative QCD. Our new threeloop contribution to this quantity forms, at not too small values of the Bjorken variable x, the dominant part of the next-to-next-to-next-to-leading order corrections. It thus facilitates improved determinations of the strong coupling α s and of 1/Q 2 power corrections from scaling violations measured in neutrino-nucleon DIS. The expansion of F 3 in powers of α s is stable at all values of x relevant to measurements at high scales Q 2 . At small x the third-order coefficient function is dominated by diagrams with the colour structure d abc d abc not present at lower orders. At large x the coefficient function for F 3 is identical to that of F 1 up to terms vanishing for x → 1.

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Section: Formalism and Calculationmentioning

confidence: 99%

Third-order QCD corrections to the charged-current structure function

2009

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“…This is the case of dimensional regularization with minimal substraction in gauge theories [14,15]. In perturbation theory, the fulfilment of the Ward identities (and of the action principle, in general) relies heavily on the following property [15,16]: the application of the kinetic differential operator to the propagator corresponding to some line in a Feynman graph is equivalent to the contraction of the line to a point. In other words, the fact that the free propagators are Green functions of the corresponding quadratic lagrangian must not be spoiled by the renormalization procedure.…”

Section: Motivation Of the Rulesmentioning

confidence: 99%

Techniques for one-loop calculations in constrained differential renormalization

et al. 1999

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“…Here the existence of the parity violating object ǫ µνλ makes the regularization nontrivial. We follow the prescription proposed by 't Hooft-Veltman [6] and systematized by Breitenlohner-Maison [7].…”

Section: Regularization Dependence Of Imaginary Part Of the Inducmentioning

confidence: 99%

“…All these regularizations differ from one another only by local terms in the gauge field. One can adopt dimensional regularization instead, regarding the totally anti-symmetric epsilon tensor as a purely three-dimensional object following the prescription proposed by 't Hooft-Veltman [6] and systematized by Breitenlohner-Maison [7]. The result comes out to be parity invariant.…”

Section: Introductionmentioning

confidence: 99%

Parity-invariant lattice regularization of a three-dimensional gauge-fermion system

Narayanan

Nishimura

1997

Nuclear Physics B

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The effective action for the gauge field induced by integrating out a massless Dirac fermion is known to give either a parity-invariant or a parity-violating result, depending on the regularization scheme. The two classes of theories cannot be connected by adding local terms in the gauge field. We construct a lattice formulation of the massless Dirac fermion using the overlap formalism. We show that the result is parity invariant in contrast to the formulation using Wilson fermions in the massless limit. This facilitates a non-perturbative study of three dimensional massless Dirac fermions interacting with a gauge field in a parity invariant setting with no need for fine-tuning.

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Dimensional renormalization and the action principle

Abstract: Dimensional renormalization is defined in such a way that the renormalized action principle holds. It is shown that this leads to a minimal, additive renormalization. The derivation of Ward-Takahashi indentities and Callan-Symanzik equations from the action principle is exemplified.

Cited by 717 publications

References 12 publications

Third-order QCD corrections to the charged-current structure function

Third-order QCD corrections to the charged-current structure function

Techniques for one-loop calculations in constrained differential renormalization

Parity-invariant lattice regularization of a three-dimensional gauge-fermion system

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