Related papers: A New Regularization Method in 3-Dimensional Momen…
The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with…
A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…
We derive a divergence formula for a group of regularization methods with an L2 constraint. The formula is useful for regularization parameter selection, because it provides an unbiased estimate for the number of degrees of freedom. We…
We propose and investigate efficient numerical methods for inverse problems related to Magnetic Resonance Imaging (MRI). Our goal is to extend the recent convergence results for the Landweber-Kaczmarz method obtained in [Haltmeier, Leitao,…
The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization.…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
In this review article we report on the newest developments in precision calculations in supersymmetric theories. An important issue related to this topic is the construction of a regularization scheme preserving simultaneously gauge…
This paper is devoted to the construction of order reduced method of fourth order problems. A framework is presented such that a problem on a high-regularity space can be deduced in a constructive way to an equivalent problem on three…
We present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the original entropy-based moment method, and this gives the…
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…
A method devised by the author is used to calculate analytical expressions for one loop integrals at finite temperature. A non-perturbative regularization of the integrals is performed, yielding expressions of non-polynomial nature. A…
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
We examine the subtleties of regularization schemes in four-dimensional space ($4S$), related in particular to the introduction of the $\gamma_5$ matrix. To illustrate we use a "Bumblebee" model featuring dynamically induced Lorentz…
One of the main difficulties in studying Quantum Field Theory, in the perturbative regime, is the calculation of D-dimensional Feynman integrals. In general, one introduces the so-called Feynman parameters and associated with them the…
A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the…
We develop a coordinate space renormalization of massless Quantum Electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier…