相关论文: Periods and Feynman integrals

The consistency of loop regularization (LORE) method is explored in multiloop calculations. A key concept of the LORE method is the introduction of irreducible loop integrals (ILIs) which are evaluated from the Feynman diagrams by adopting…

We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the…

A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…

We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…

We review certain classes of iterated integrals that appear in the computation of Feynman integrals that involve elliptic functions. These functions generalise the well-known class of multiple polylogarithms to elliptic curves and are…

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master…

A connection between one-loop $N$-point Feynman diagrams and certain geometrical quantities in non-Euclidean geometry is discussed. A geometrical way to calculate the corresponding Feynman integrals is considered. (This paper contains a…

Based on the method developed in [K.~H.~Phan and T.~Riemann, Phys.\ Lett.\ B {\bf 791} (2019) 257], detailed analytic results for scalar one-loop two-, three-, four-point integrals in general $d$-dimension are presented in this paper. The…

We consider Feynman integrals with algebraic leading singularities and total differentials in $\epsilon\,\mathrm{d}\ln$ form. We show for the first time that it is possible to evaluate integrals with singularities involving unrationalizable…

We study multivariate Mellin transforms of Laurent polynomials by considering special toric compactifications which make their singular structure apparent. This gives a precise description of their convergence domain, refining results of…

Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory. They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for…

A detailed investigation is presented of a set of algorithms which form the basis for a fast and reliable numerical integration of one-loop multi-leg (up to six) Feynman diagrams, with special attention to the behavior around (possibly)…

Let $f$ be a Laurent polynomial in two variables, whose Newton polygon strictly contains the origin and whose vertices are primitive lattice points, and let $L_f$ be the minimal-order differential operator that annihilates the period…

We describe differential forms representing Feynman amplitudes in configuration spaces of Feynman graphs, and regularization and evaluation techniques, for suitable chains of integration, that give rise to periods of mixed Tate motives.

We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and…

We develop a renormalisation scheme for time--ordered products in interacting field theories on curved spacetimes which consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This…

A Feynman period is a particular residue of a scalar Feynman integral which is both physically and number theoretically interesting. Two ways in which the graph theory of the underlying Feynman graph can illuminate the Feynman period are…

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…

We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FIs computation is conceptually changed to a linear algebraic problem. Examples up…