A four-dimensional approach to quantum field theories

Abstract

I present a novel Four-Dimensional Regularization/Renormalization approach (FDR) to ultraviolet divergences in field theories which can be interpreted as a natural separation between physical and non physical degrees of freedom. Based on the observation that some infinities can be reabsorbed into the vacuum expectation value of the fields, rather than into the parameters of the Lagrangian, a new type of four-dimensional loop integral is introduced (the FDR integral) which is independent of any UV regulator and respects all properties required by gauge invariance. FDR reproduces the correct ABJ anomaly and no change in the definition of gamma_5 is needed. With FDR the possibility is open for an approach to UV infinities in which the renormalization program is substituted by a simple reinterpretation of the appearing loop integrals as FDR ones, leading to important consequences in the context of non-renormalizable field theories. Finally, I show how FDR can also be used to regularize infrared and collinear divergences.

25 pages, 12 figures. A few misprints corrected. Accepted by JHEP

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Cited by in corpus (41)

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• May the four be with you: Novel IR-subtraction methods to tackle NNLO calculations
• Mathematical properties of nested residues and their application to multi-loop scattering amplitudes
• Gauge invariance at work in FDR: H -> gamma gamma
• Causal representation of multi-loop Feynman integrands within the loop-tree duality
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Loop-tree duality from vertices and edges
• FDR, an easier way to NNLO calculations: a two-loop case study
• Dimensional regularization vs methods in fixed dimension with and without ${\gamma }_5$
• Two-loop off-shell QCD amplitudes in FDR
• QCD corrections to H -> gg in FDR
• Universal opening of four-loop scattering amplitudes to trees
• Two-Loop Rational Terms in Yang-Mills Theories
• Rational Terms of UV Origin at Two Loops
• Computation of $H\to gg$ in FDH and DRED: renormalization, operator mixing, and explicit two-loop results
• Regularization-scheme dependence of QCD amplitudes in the massive case
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• R2 vertices for the effective ggH theory
• Two-loop renormalisation of gauge theories in $4D$ Implicit Regularisation and connections to dimensional methods
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• Sensitivity of the decay $h\to Z{Z}^{\ast }\to Zl+l-$ to the Higgs self coupling through radiative corrections
• A step towards a consistent treatment of chiral theories at higher loop order: the abelian case
• NNLO final-state quark-pair corrections in four dimensions
• On the predictivity of the non-renormalizable quantum field theories
• Direct numerical evaluation of multi-loop integrals without contour deformation
• One-loop decays $A^0\to ZZ,Z\gamma ,\gamma \gamma$ within the 2HDM and its search at the LHC
• Integration-by-parts identities in FDR
• Supercurrent anomaly and gauge invariance in N=1 supersymmetric Yang-Mills theory
• Quadratic Contributions of Softly Broken Supersymmetry in the Light of Loop Regularization
• Infrared Subtleties and Chiral Vertices at NLO: An Implicit Regularization Analysis
• Numerical Evaluation of Two-Loop Integrals in FDR
• Dimensional schemes for cross sections at NNLO
• Line shape and the experimental determination of the $J/\psi \to \gamma {\eta }_c$ branching fraction
• Monte Carlo evaluation of divergent one-loop integrals without contour deformation
• The $\gamma \gamma$ decay of the Higgs boson in FDR
• Finite Z-less integral expressions for $\beta$-functions in the MS4 scheme
• Two-Loop Rational Terms for Spontaneously Broken Theories