On the equivalence between Implicit Regularization and Constrained Differential Renormalization

Abstract

Constrained Differential Renormalization (CDR) and the constrained version of Implicit Regularization (IR) are two regularization independent techniques that do not rely on dimensional continuation of the space-time. These two methods which have rather distinct basis have been successfully applied to several calculations which show that they can be trusted as practical, symmetry invariant frameworks (gauge and supersymmetry included) in perturbative computations even beyond one-loop order. In this paper, we show the equivalence between these two methods at one-loop order. We show that the configuration space rules of CDR can be mapped into the momentum space procedures of Implicit Regularization, the major principle behind this equivalence being the extension of the properties of regular distributions to the regularized ones.

16 pages

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Cited by in corpus (16)

• To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
• Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED
• Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams
• Quantum gravitational contributions to the beta function of quantum electrodynamics
• (Un)determined finite regularization dependent quantum corrections: the Higgs decay into two photons and the two photon scattering examples
• Regularization Independent Analysis of the Origin of Two Loop Contributions to N=1 Super Yang-Mills Beta Function
• Dimensional regularization vs methods in fixed dimension with and without ${\gamma }_5$
• Implicit regularization beyond one loop order: gauge field theories
• Momentum routing invariance in Feynman diagrams and quantum symmetry breakings
• Systematization of Basic Divergent Integrals in Perturbation Theory and Renormalization Group Functions
• Momentum Routing Invariance in Extended QED: Assuring Gauge Invariance Beyond Tree Level
• Two-loop renormalisation of gauge theories in $4D$ Implicit Regularisation and connections to dimensional methods
• Guises and Disguises of Quadratic Divergences
• Naturalness and theoretical constraints on the Higgs boson mass
• Ultraviolet and Infrared Divergences in Implicit Regularization: a Consistent Approach
• Coordinate space representation for renormalization of quantum electrodynamics