Related papers: On Finite Representation of Dimensionally Regulari…
We present a closed-form finite-dimensional projection method for regularizing a function defined by a discrete set of measurement data, which have been contaminated by random, zero mean errors, and for estimating the derivative and…
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…
Reference [1] introduces a method for computing numerically four-dimensional multi-loop integrals without performing an explicit analytic contour deformation around threshold singularities. In this paper, we extend such a technique to…
The infrared divergent scalar three-point integrals are evaluated by the loop regularization method. Three kinds of infrared divergent integrals, i.e., massless triangle diagram, triangle diagrams with one and two massive internal lines,…
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 have recently proposed a new regularization framework based on the loop-tree duality theorem. This theorem allows to rewrite loop level amplitudes in terms of tree-level structures and phase-space integrations. In consequence, it is…
We introduce a new regularization scheme for divergent integrals in quantum field theory. The framework is based on the structural decomposition of the integrand asymptotic expansion, which distinguishes between contributions that drive UV…
A general method for calculating asymptotic expansions of infinite sums in thermal field theory is presented. It is shown that the Mellin summation method works elegantly with dimensional regularization. A general result is derived for a…
We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the…
In this work, we mainly study the one-loop effective action for real scalar theories in non-homogeneous backgrounds in odd dimensions. It is shown that through the method studied in Ref. [1], it is possible to obtain a unified result for…
Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not…
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…
We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…
Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory. They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for…
An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the…
We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…
We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on…
Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…
A set of one-loop vertex and box tensor-integrals with massless internal particles has been obtained directly without any reduction method to scalar-integrals. The results with one or two massive external lines for the vertex integral and…
Renormalization is a well-known technique to get rid of ultraviolet (UV) singularities. When relying on Dimensional Regularization (DREG), these become manifest as $\epsilon$-poles, allowing to define counter-terms with useful recursive…