Related papers: Dimensional Reduction and Hadronic Processes
We discuss how to apply regularization by dimensional reduction for computing hadronic cross sections at next-to-leading order. We analyze the infrared singularity structure, demonstrate that there are no problems with factorization, and…
So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of…
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon…
I apply commonly used regularization schemes to a multi-loop calculation to examine the properties of the schemes at higher orders. I find complete consistency between the conventional dimensional regularization scheme and dimensional…
We describe the equivalence at one loop between constrained differential renormalization and regularization by dimensional reduction in the MS scheme. To illustrate it, we reexamine the calculation of supergravity corrections to (g-2)_l.
It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…
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 apply the dimensional regularization procedure to treat an ultraviolet divergence occurring in the framework of the nuclear many-body problem. We consider the second--order correction (beyond the mean-field approximation) to the equation…
We demonstrate that almost all non-parametric dimensionality reduction methods can be expressed by a simple procedure: regularized loss minimization plus singular value truncation. By distinguishing the role of the loss and regularizer in…
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…
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…
Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
Dimensional regularization is applied to the Lippmann-Schwinger equation for a separable potential which gives rise to logarithmic singularities in the Born series. For this potential a subtraction at a fixed energy can be used to…
Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences…
We analyze a new approach to Machine Learning coming from a modification of classical regularization networks by casting the process in the time dimension, leading to a sort of collapse of dimensionality in the problem of learning the model…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
We discuss the dependence of running couplings on the choice of regularization method in a general softly-broken N=1 supersymmetric theory. Regularization by dimensional reduction respects supersymmetry, but standard dimensional…