Related papers: Notes on Feynman Integrals and Renormalization
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…
We study differential equations for Feynman amplitudes and we show that the corresponding D-module is isomorphic to a GKZ D-modules. We show that the sheaf of solutions to the D-module is isomorphic to a certain relative homology and the…
We present a partial survey on normal numbers, including Keane's contributions, and with recent developments in different directions.
This is a conceptual paper that re-examines the principles underlying the application of renormalization theory to quantum phase transitions in the light of quantum information theory. We start by describing the intuitive argument known as…
We give an overview of state-of-the-art multi-loop Feynman diagram computations, and explain how we use symbolic manipulation to generate renormalized integrals that are then evaluated numerically. We explain how we automate BPHZ…
A method for computing singular or nearly singular integrals on closed surfaces was presented by J. T. Beale, W. Ying, and J. R. Wilson [Comm. Comput. Phys. 20 (2016), 733--753, arXiv:1508.00265] and applied to single and double layer…
Our main purpose is to give multiple examples for using the available implementations for computing the normalization of an affine ring, computing the minimial generators of the normalization as an algebra over the original ring and…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
The method of brackets, consisting of a small number of heuristic rules, was created by Ivan Gonzalez for the evaluation of definite integrals appearing in the resolution of Feynman diagrams. The current work verifies each step of this…
In my PHD thesis I present a method for the off-shell singularity analysis of Feynman amplitudes based on the Speer sector decomposition of the Schwinger parametric integrals combined with the Mellin-Barnes tranform. I apply the method to…
We describe how a dlog representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized…
Various uses of the renormalization group are examined.
We develop a geometric framework in Feynman-parameter space to determine constraints on the sequential discontinuities of Feynman integrals. Our method is based on tracking the deformation of the integration contour as external kinematics…
In this article, I give a pedagogical introduction and overview of percolation theory. Special emphasis will be put on the review of some of the most prominent of the algorithms that have been devised to study percolation numerically. At…
The Coulomb gauge in nonabelian gauge theories is attractive in principle, but beset with technical difficulties in perturbation theory. In addition to ordinary Feynman integrals, there are, at 2-loop order, Christ-Lee (CL) terms, derived…
Various forms of regularization in learning tasks strive for different notions of simplicity. This paper presents a spectral regularization technique, which attaches a unique inductive bias to sequence modeling based on an intuitive concept…
I discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method.
We provide a self-contained formulation of the BPHZ theorem in the Euclidean context, which yields a systematic procedure to "renormalise" otherwise divergent integrals appearing in generalised convolutions of functions with a singularity…
In this brief article I show how the notion of coarse graining and the Renormalization Group enter naturally in the dynamics of genetic systems, in particular in the presence of recombination. I show how the latter induces a dynamics…
Parametric Feynman integrals with the regions of integration defined by some polynomials are considered in this paper. It is shown that integrals with irregular integration regions can be converted to standard parametric integrals, for…