相关论文: Loop Integrals, R Functions and their Analytic Con…
This paper presents an evaluation of the wave function coefficients for conformally coupled scalars at both one and two-loop levels at leading order in the coupling constant, in momentum space. We take cues from time-dependent interactions…
In the kinematic region where three particles $i$, $j$, $k$ are collinear, the multi-parton scattering amplitudes factorise into a product of a triple collinear splitting function and a multi-parton scattering amplitude with two fewer…
The soft and collinear singularities of general scalar and tensor one-loop N-point integrals are worked out explicitly. As a result a simple explicit formula is given that expresses the singular part in terms of 3-point integrals. Apart…
We present master formulas for the divergent part of the one-loop effective action for an arbitrary (both minimal and nonminimal) operators of any order in the 4-dimensional curved space. They can be considered as computer algorithms,…
We apply set-valued numerical methods to compute an accurate enclosure of the rotation number. The described algorithm is supplemented with a method of proving the existence of periodic points, which is used to check the rationality of the…
We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to…
We develop integration theory for integrating functions taking values into a Dedekind complete unital $f$-algebra $\mathbb{L}$ with respect to $\mathbb{L}$-valued measures. We then discuss and prove completeness results of…
The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the hole complex plane. In this paper, certain cases of specific (non-real analytic) smooth functions…
In the present article we describe a class of algebraic curves on which rational functions of two arguments may reach all their possible limiting values. We also solve a similar question for functions that can be represented as a uniform…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
New analytic formulas for one-loop three-point Feynman integrals in general space-time dimension ($d$) are presented in this paper. The calculations are performed at general configurations for internal masses and external momenta. The…
Highly oscillatory integrals, such as those involving Bessel functions, are best evaluated analytically as much as possible, as numerical errors can be difficult to control. We investigate indefinite integrals involving monomials in $x$…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
For a given elliptic curve, its associated $L$-function evaluated at $1$ is closely related to its real period. In this article, we generalize this principle to a rational curve. We count the rational points over all finite fields and use…
One-loop integrands can be written in terms of a simple, process-independent basis. We show that a similar basis exists for integrands of phase-space integrals for the real-emission contribution at next-to-leading order. Our demonstration…
We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.