On the predictivity of the non-renormalizable quantum field theories

Abstract

Following a Four Dimensional Renormalization approach to ultraviolet divergences (FDR), we extend the concept of predictivity to non-renormalizable quantum field theories at arbitrarily large perturbative orders. The idea of topological renormalization is introduced, which keeps a finite value for the parameters of the theory by trading the usual order-by-order renormalization procedure for an order-by-order redefinition of the perturbative vacuum. One additional measurement is then sufficient to systematically compute quantum corrections at any loop order, with no need of absorbing ultraviolet infinities in the Lagrangian.

Paper reorganized

References in corpus (6)

• A four-dimensional approach to quantum field theories
• Gauge invariance at work in FDR: H -> gamma gamma
• A Massive Yang-Mills Theory based on the Nonlinearly Realized Gauge Group
• FDR, an easier way to NNLO calculations: a two-loop case study
• QCD corrections to H -> gg in FDR
• Integration-by-parts identities in FDR

Cited by in corpus (7)

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• QCD corrections to H -> gg in FDR
• NNLO final-state quark-pair corrections in four dimensions
• Integration-by-parts identities in FDR
• Line shape and the experimental determination of the $J/\psi \to \gamma {\eta }_c$ branching fraction
• Matching high-energy electroweak fermion loops onto the Fermi theory without higher dimensional operators