相关论文: On dimensional regularization and mathematical rig…

We consider regularisation of a Yang-Mills theory by Dimensional Reduction (DRED). In particular, the anomalous dimensions of fermion masses and gauge coupling are computed to four-loop order. We put special emphasis on the treatment of…

We give insight into the critical problem of an open resonator that is subject to a perturbation outside of its cavity region. We utilize the framework of quasinormal modes (QNMs), which are the natural mode solutions to the open boundary…

Proceeding by way of examples, we update the combinatorics of the treatment of Feynman diagrams with subdivergences in differential renormalization from more recent viewpoints in Epstein--Glaser renormalization in $x$-space.

For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional…

We explicitly construct fractals of dimension 4-epsilon on which dimensional regularization approximates scalar-field-only quantum-field-theory amplitudes. The construction does not require fractals to be Lorentz-invariant in any sense, and…

A brief review of recent results on analytical evaluation of double-box Feynman integrals is presented. First steps towards evaluation of massless on-shell triple-box Feynman integrals within dimensional regularization are described. The…

The volume of the distribution of weight sets associated with a loss value may be the source of implicit regularization from overparameterization due to the phenomenon of contracting volume with increasing dimensions for geometric figures…

While it is usually stated that dimensional regularization (DR) has no direct physical interpretation, consensus has recently grown on the idea that it might be endowed with special physical properties that would provide the mechanism that…

In view of various field-theoretic reasons, in the present work, we study the question of if the usual dimensional regularization can be extended to quantum field theories with an ultraviolet cutoff (Poincare-breaking scale) in a way…

Explicit formulae for asymptotic expansions of Feynman diagrams in typical limits of momenta and masses with external legs on the mass shell are presented.

We study the regularization ambiguities in an exact renormalized (1+1)-dimensional field theory. We show a relation between the regularization ambiguities and the coupling parameters of the theory as well as their role in the implementation…

We show that there is a very simple relationship between differential and dimensional renormalization of low-order Feynman graphs in renormalizable massless quantum field theories. The beauty of the differential approach is that it achieves…

Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…

Perturbative expansions in quantum field theory diverge for at least two reasons: the number of Feynman diagrams increases dramatically with the loop number and the process of renormalization may make the contribution of some diagrams…

This Note derives regularity bounds for a Gevrey criterion when the Cauchy problem of elliptic equations is solved by regularization. When utilizing the regularization, one knows that checking such criterion is basically problematic, albeit…

We review the concept of infinity as applied to regularization procedures in Quantum Electrodynamics. A clear distinction that is lacking in current literature is made between the physical contents of renormalization, and the mathematical…

General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.

We present a general analysis of the field theoretical properties which guarantee the recovery, at the renormalized level, of symmetries broken by regularization. We also discuss the anomalous case.

Hypergeometric functions provide a useful representation of Feynman diagrams occuring in precision phenomenology. In dimension regularization, the epsilon-expansion of these functions about d=4 is required. We discuss the current status of…

The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an…