Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams

Abstract

Implicit Regularization (IReg) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IReg program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multi-loop amplitude in a well defined set of basic divergent integrals in one loop momentum only which is the essence of IReg. Moreover, we conjecture that momentum routing invariance in the loops, which has been shown to be connected with gauge symmetry, is a fundamental symmetry of any Feynman diagram in a renormalizable quantum field theory.

References in corpus (16)

• Chiral Anomaly and CPT invariance in an implicit momentum space regularization framework
• A hint of renormalization
• Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED
• Consistency Relations for an Implicit n-dimensional Regularization Scheme
• Consistency in Regularizations of the Gauged NJL Model at One Loop Level
• Implicit Regularization and Renormalization of QCD
• Comparing Implicit, Differential, Dimensional and BPHZ Renormalisation
• Regularization Independent Analysis of the Origin of Two Loop Contributions to N=1 Super Yang-Mills Beta Function
• Implicit regularization beyond one loop order: gauge field theories
• Arbitrary parameters in implicit regularization and democracy within perturbative description of 2-dimensional gravitational anomalies
• Supergravity corrections to the $(g-2{)}_l$ factor by Implicit Regularization
• On the equivalence between Implicit Regularization and Constrained Differential Renormalization
• The Role of hidden ambiguities in the Linear Sigma Model with fermions
• Symmetries and Ambiguities in the linear sigma model with light quarks
• Implicit regularization beyond one loop order: scalar field theories
• Ultraviolet and Infrared Divergences in Implicit Regularization: a Consistent Approach

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