Related papers: A New Regularization Method in 3-Dimensional Momen…
In this paper, we present a dynamic non-diagonal regularization for interior point methods. The non-diagonal aspect of this regularization is implicit, since all the off-diagonal elements of the regularization matrices are cancelled out by…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems…
A unified formulation of one-loop tensor integrals is proposed for systematical calculations of finite volume corrections. It is shown that decomposition of the one-loop tensor integrals into a series of tensors accompanied by tensor…
Implicit Regularization is a 4-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional…
A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…
A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension $d$ is proposed. The relation between $d$ and $d-2$ dimensional integrals is given in terms of a…
This paper is a continuation of our earlier work \cite{NRxx} in which a numerical moment method with arbitrary order of moments was presented. However, the computation may break down during the calculation of the structure of a shock wave…
In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…
The calculation of loop amplitudes with parity violation or spin effects within dimensional regularization needs a consistent definition of gamma5. Also loop calculations in supersymmetric theories need a consistent definition of gamma5. In…
We present a method to numerically evaluate infrared-finite one- and two-loop integrals within the Four-Dimensional Regularization/Renormalization approach, in which a small mass serves as regulator. Typical integrals exhibit a logarithmic…
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…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
In the paper, we study the two-loop contribution to the effective action of the four-dimensional quantum Yang-Mills theory. We derive a new formula for the contribution in terms of three functions, formed from the Green's function expansion…
We present a new method for the calculation of differential distributions directly in Mellin space without recourse to the usual momentum-fraction (or z-) space. The method is completely general and can be applied to any process. It is…
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…
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…
It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.
We describe in some detail the present features of an automatic loop calculation program as well as the integration techniques that go into it. The program, called XLOOPS 1.0, allows one to calculate massive one- and two-loop Feynman…