Related papers: Cutkosky representation and direct integration
We introduce a novel method for encoding integers using smooth real-valued functions whose integral properties implicitly reflect discrete quantities. In contrast to classical representations, where the integer appears as an explicit…
We take a fresh look at Feynman diagrams in the spinor-helicity formalism. Focusing on tree-level massless QED and QCD, we develop a new and conceptually simple graphical method for their calculation. In this pictorial method, which we dub…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Equilibrium measures are special invariant measures of chaotic dynamical systems and iterated function systems, commonly studied as salient examples of fractal measures. While useful analytic expressions are rare, computational exploration…
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
Evaluating gravitational path integrals in the Lorentzian has been a long-standing challenge due to the numerical sign problem. We show that this challenge can be overcome in simplicial quantum gravity. By deforming the integration contour…
We present a generally applicable reduction formalism which makes it possible to express an arbitrary tensor and scalar one-loop Feynman integral, with N external lines and massless propagators, in terms of a basic set of eight fundamental…
We present a class of exponential integrators to compute solutions of the stochastic Schr\"odinger equation arising from the modeling of open quantum systems. In order to be able to implement the methods within the same framework as the…
In this paper we investigate the representation of a class of non Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential…
We adapt the direct approach to the semiclassical Bergman kernel asymptotics, developed recently by A. Deleporte, J. Sj\"ostrand, and the first-named author for real analytic exponential weights, to the smooth case. Similar to that work,…
An approach to approximate evaluation of the continuum Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are…
We overview recent results on the mathematical foundations of Cutkosky rules. We emphasize that the two operations of shrinking an internal edge or putting internal lines on the mass-shell are natural operation on the cubical chain complex…
Weighted norm estimates and representation formulas are proved for non-homogeneous singular integrals with no regularity condition on the kernel and only an L log L integrability condition. The representation formulas involve averages over…
An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting…
A famous result due to Ko and Friedman (1982) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sense. Yet, both functionals are routinely computed at great…
The integral $\int_0^a f(t) t^{-s} \mathrm{d}t$ diverges for $\text{Re}(s) \geq \lambda + 1$, where $\lambda$ is the order of the first non-vanishing derivative of $f(t)$ at the origin. With the assumption that $f(t)$ is analytic at the…
Every finite-dimensional unitary representation of the N-extended worldline supersymmetry without central charges may be obtained by a sequence of differential transformations from a direct sum of minimal Adinkras, simple supermultiplets…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. We in particular discuss decomposition methods, which reduce the problem to a number of…
Derivative of a function can be expressed in terms of integration over a small neighborhood of the point of differentiation, so-called differentiation by integration method. In this text a maximal generalization of existing results which…