Related papers: Extensions in FormCalc 5.3
A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is intended to serve as a link between quantum and classical field theories, resulting in an independent constructive characterisation of the…
A geometrical way to calculate N-point Feynman diagrams is reviewed. As an example, the dimensionally-regulated three-point function is considered, including all orders of its epsilon-expansion. Analytical continuation to other regions of…
In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic…
In this article, we present the package {\tt Blade} as the first implementation of the block-triangular form improved Feynman integral reduction method. The block-triangular form has orders of magnitude fewer equations compared to the plain…
Some problems related to construction of the epsilon-expansion of dimensionally regulated Feynman integrals are discussed. For certain classes of diagrams, an arbitrary term of the epsilon-expansion can be expressed in terms of log-sine…
The Kalman filter and its extensions are used in a vast number of aerospace and navigation applications for nonlinear state estimation of time series. In the literature, different approaches have been proposed to exploit the structure of…
This tutorial introduces (and provides, via the document source) the Quantikz LaTeX package for typesetting quantum circuit diagrams. This takes advantage of tikz to give greater control over the circuit options. Those familiar with the…
This work introduces a new software package `Sesame' for the numerical computation of classical semiconductor equations. It supports 1 and 2-dimensional systems and provides tools to easily implement extended defects such as grain…
Fact-checking on the Web has become the main mechanism through which we detect the credibility of the news or information. Existing fact-checkers verify the authenticity of the information (support or refute the claim) based on secondary…
The present paper provides a method for finding partial differential equations satisfied by the Feynman integrals for diagrams of various types, using the Griffiths theorem on the reduction of poles of rational differential forms. As an…
We develop closed form expressions for various finite binomial Fibonacci and Lucas sums depending on the modulo 5 nature of the upper summation limit. Our expressions are inferred from some trigonometric identities.
We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…
A process of extending sets which can be used as foundation for an alternative organization for Differential and Integral Calculus is presented.
We give the extension formulae on almost complex manifolds and give decompositions of the extension formulae. As applications, we study $(n,0)$-forms, the $(n,0)$-Dolbeault cohomology group and $(n,q)$-forms on almost complex manifolds.
Particle symbols and Feynman diagrams often used in particle physics can be generated by a word document processor. Standard office packages have their built in symbols such as solid-line, dashed-line, arrows, etc. which are also used in…
The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the…
We extend Gegenbauer Polynomials technique to evaluate a class of complicated Feynman diagrams. New results in the form of $_3F_2$-hypergeometrical series of unit argument, are presented. As a by-product, we present a new transformation…
We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…
In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and…
This work presents an updated version of the previously released freeware MAN (Modal Analysis of Nanoresonators) [Comput Phys Commun 284, 108627 (2023)], a software package designed to efficiently compute and normalize quasinormal modes…