Related papers: On dimensional regularization and mathematical rig…
In this talk we show that dual conformal symmetry has unexpected applications to Feynman integrals in dimensional regularization. Outside $4$ dimensions, the symmetry is anomalous, but still preserves the unitarity cut surfaces. This…
We extend an implicit regularization scheme to be applicable in the $n$-dimensional space-time. Within this scheme divergences involving parity violating objects can be consistently treated without recoursing to dimensional continuation.…
I review various aspects of Feynman integrals, regularization and renormalization. Following Bloch, I focus on a linear algebraic approach to the Feynman rules, and I try to bring together several renormalization methods found in the…
We provide a brief outlook on recent developments in regularity theory for nonuniformly elliptic problems, with special emphasis on those of variational nature.
A certain pattern of divergence of perturbative expansions in quantum field theories, related to their small and large momentum behaviour, is known as renormalons. We review formal and phenomenological aspects of renormalon divergence. We…
Higher-order diagrams required for radiative corrections to mixed electroweak and QCD processes at the LHC and anticipated future colliders will require numerically stable representations of the associated Feynman diagrams. The…
The absence of the quadratic divergence in the Higgs sector of the Standard Model in the dimensional regularization is usually regarded to be an exceptional property of a specific regularization. To understand what is going on in the…
We discuss issues that arise in the regularisation of supersymmetric theories. (To appear in the book `Perspectives on Supersymmetry', World Scientific, Editor G. Kane.)
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
The use of the dimensional regularization in the on-mass-shell renormalization scheme sometimes fails to locally cancel the ultraviolet divergence for a class of diagrams in the two-loop order. The mechanism is discussed based on an example…
Three-dimensional cutoff regulators are frequently employed in multi-nucleon calculations, but they violate chiral symmetry and Lorentz invariance. A cutoff regularization scheme is proposed to compensate systematically at subleading orders…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…
An arbitrary term of the epsilon-expansion of dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using magic connection between these…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
The divergence of perturbative expansions for the vast majority of macroscopic systems, which follows from Dyson's collapse argument, prevents Feynman's diagrammatic technique from being directly used for controllable studies of strongly…
We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the…
Recent developments in higher order calculations within the framework of Dimensional Reduction, the preferred regularization scheme for supersymmetric theories, are reported on. Special emphasis is put on the treatment of evanescent…
We investigate the issue of regularization/renormalization in the presence of a nontrivial background in the case of 1+1-(supersymmetric) solitons. In particular we study and compare the commonly employed regularization methods (mode-…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
Problems that arise in the application of general prescriptions of the so-called strategy of regions for asymptotic expansions of Feynman integrals in various limits of momenta and masses are discussed with the help of characteristic…