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 (7)

• Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED
• 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
• On the equivalence between Implicit Regularization and Constrained Differential Renormalization
• Supergravity corrections to the $(g-2{)}_l$ factor by Implicit Regularization
• The Role of hidden ambiguities in the Linear Sigma Model with fermions
• Implicit regularization beyond one loop order: scalar field theories

Cited by in corpus (2)

• A four-dimensional approach to quantum field theories
• (Un)determined finite regularization dependent quantum corrections: the Higgs decay into two photons and the two photon scattering examples