A comment on the relationship between differential and dimensional renormalization

Dunne, Gerald V.; Rius, Nuria

doi:10.1016/0370-2693(92)90897-d

Cited by 25 publications

(23 citation statements)

References 18 publications

(31 reference statements)

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“…Then, diagram K 2 of Fig. 2 vanishes identically, while diagram K 2 directly gives (6.40) plus a pole in 1/(d − 4), which is cancelled by a local counterterm, see [36,37]. The same result can be found even more directly, without explicit regularisation, in differential renormalisation [35].…”

Section: Renormalisationmentioning

confidence: 66%

Wilsonian renormalisation of CFT correlation functions: field theory

Lizana

Pérez-Victoria

2017

J. High Energ. Phys.

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Abstract:We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space allows us to select convenient non-linear parametrisations that serve different purposes. First, we identify normal parameters in which the renormalisation group flows take their simplest form; normal correlators are defined by functional differentiation with respect to these parameters. The renormalised correlation functions are given by the continuum limit of correlators associated to a cutoff-dependent parametrisation, which can be related to the renormalisation group flows. The necessary linear and non-linear counterterms in any arbitrary parametrisation arise in a natural way from a change of coordinates. We show that, in a class of minimal subtraction schemes, the renormalised correlators are exactly equal to normal correlators evaluated at a finite cutoff. To illustrate the formalism and the main results, we compare standard diagrammatic calculations in a scalar free-field theory with the structure of the perturbative solutions to the Polchinski equation close to the Gaussian fixed point.

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Section: Renormalisationmentioning

confidence: 66%

Wilsonian renormalisation of CFT correlation functions: field theory

Lizana

Pérez-Victoria

2017

J. High Energ. Phys.

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“…It is a simple task to verify that CIR explicitly preserves the Slavnov-Taylor identities expressed by (15):…”

Section: Slavnov-taylor Identities and Renormalization Group Funmentioning

confidence: 99%

“…In [8] we compare renormalization schemes in IR, DR and differential renormalization (see also [15]). …”

Section: Loop Qcd In Implicit Regularizationmentioning

confidence: 99%

Implicit Regularization and Renormalization of QCD

Sampaio

Scarpelli²,

Ottoni³

et al. 2006

Int J Theor Phys

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“…We should here note that Differential Renormalization (DR) procedure [34,35], which has been vastly investigated in the literature, is done in coordinate space, though the traditional method of renormalization in momentum space (for review see [36,37]). DR is equivalent to traditional renormalization [38][39][40], and is based on the observation that the UV divergence reflects in the fact that the higher order amplitude cannot have a Fourier transform into momentum space due to the short-distance singularity. Thus one can, first, regulate such an amplitude by writing its singular parts as the derivatives of the normal functions, which have well defined Fourier transformation, and second, by performing the Fourier transformation in partial integration and discarding the surface term, directly get the renormalized result.…”

Section: Introductionmentioning

confidence: 99%

Coordinate space representation for renormalization of quantum electrodynamics

Mojavezi,

Moazzemi,

Zomorrodian

2020

Preprint

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In this paper we present a systematic treatment for fundamental renormalization of quantum electrodynamics in real space. Although the standard renormalization is an old school problem in this case, it has not yet been completely done in position space. The most important difference with well-known differential renormalization is that we do the whole procedure in coordinate space without need to transformation to momentum space. Specially, we directly derive the conterterms in real space. This problem becomes important when the translational symmetry of the system breaks somehow explicitly (for example by nontrivial boundary condition (BC) on the fields). In this case, one is not able to move to momentum space by a simple Fourier transformation. Therefore, in the context of renormalized perturbation theory, by imposing the renormalization conditions, counterterms in coordinate space will depend directly on the fields BCs (or background topology). Trivial BC or trivial background lead to the usual standard conterterms. If the counterterms modify then the quantum corrections of any physical quantity are different from those in free space where we have the translational invariance. We also show that, up to order α, our counterterms are reduced to usual standard terms derived in free space.

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A comment on the relationship between differential and dimensional renormalization

Cited by 25 publications

References 18 publications

Wilsonian renormalisation of CFT correlation functions: field theory

Wilsonian renormalisation of CFT correlation functions: field theory

Implicit Regularization and Renormalization of QCD

Coordinate space representation for renormalization of quantum electrodynamics

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