Related papers: On Finite Representation of Dimensionally Regulari…
The worldline formalism offers an alternative framework to the standard diagrammatic approach in quantum field theory, grounded in first-quantized relativistic path integrals. Over recent decades, this formalism has attracted growing…
In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper…
The problem of UV divergences in QFT has long been a fundamental challenge. Standard regularization techniques modify high-energy behavior to ensure well-defined integrals. However, these approaches often introduce unphysical parameters,…
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…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
We review the Four-Dimensional-Formulation variant of the Four-Dimensional-Helicity scheme, by showing two applications of this regularisation scheme. The first one is the computation of one-loop helicity amplitudes, for which we present…
An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for 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 compare a momentum space implicit regularisation (IR) framework with other renormalisation methods which may be applied to dimension specific theories, namely Differential Renormalisation (DfR) and the BPHZ formalism. In particular, we…
We illustrated via the sunset diagram that dimensional regularization 'deforms' the nonlocal contents of multi-loop diagrams with its equivalence to cut-off regularization scheme recovered only after sub-divergence were subtracted. Then we…
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point…
Depth estimation is an essential component in understanding the 3D geometry of a scene, with numerous applications in urban and indoor settings. These scenes are characterized by a prevalence of human made structures, which in most of the…
The resummed expression for the quark form factor illustrates the fact that dimensional continuation provides a regularization not only for ultraviolet and infrared singularities of fixed order QCD amplitudes, but also for the Landau pole…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
It is shown that a simple modification of the dimensional regularization allows to compute in a consistent and gauge invariant way any diagram with less than four loops in the SO(10) unified model. The method applies also to the Standard…
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…
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of…
We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the…
We propose a numerical method based on the master field for large-$N$ reduced matrix models. While the master field is originally an infinite-dimensional matrix, in this method it is regularized to a finite dimension, with the requirement…
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can…