Related papers: A closed expression for the UV-divergent parts of …

We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the…

We study $n$-point functions at finite temperature in the closed time path formalism. With the help of two basic column vectors and their dual partners we derive a compact decomposition of the time-ordered $n$-point functions with $2^n$…

We present a prescription for choosing orthogonal bases of differential $n$-forms belonging to quadratic twisted period integrals, with respect to the intersection number inner product. To evaluate these inner products, we additionally…

We introduce an efficient configuration space technique which allows one to compute a class of Feynman diagrams which generalize the scalar sunset topology to any number of massive internal lines. General tensor vertex structures and…

Recently a non-perturbative formula for the RG flow between UV and IR fixed points of the coefficient in the trace of the energy momentum tensor of the Euler density has been obtained for N=1 SUSY gauge theories by relating the trace and…

Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…

In four-dimensional theories with massless particles, the one-loop amplitudes can be expressed in terms of a basis of scalar integrals and rational terms. Since the scalar bubble integrals are the only UV divergent integrals, the sum of the…

This paper is concerned with the low Tucker-rank tensor completion problem, which is about reconstructing a tensor $ T \in\mathbb{R}^{n\times n \times n}$ of low multilinear rank from partially observed entries. Riemannian optimization…

A precise calculation of the lepton anomalous magnetic moments (AMM) requires an evaluation of the quantum electrodynamics (QED) Feynman diagrams up to five independent loops. The complicated structure of ultraviolet (UV), infrared (IR) and…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

We compute radiative corrections in five and six dimensional field theories, using winding modes in mixed momentum-coordinate space. This method provides a simple way of finding UV divergencies, finite corrections and localized terms when…

Using functional derivatives with respect to free propagators and interactions we derive a closed set of Schwinger-Dyson equations in quantum electrodynamics. Its conversion to graphical recursion relations allows us to systematically…

First principles approaches have revolutionized our ability in using computers to predict, explore and design materials. A major advantage commonly associated with these approaches is that they are fully parameter free. However, numerically…

A Feynman formula is a representation of a solution of an initial (or initial-boundary) value problem for an evolution equation (or, equivalently, a representation of the semigroup resolving the problem) by a limit of $n$-fold iterated…

I present calculations of two-loop vertex corrections with massive and massless partons in the eikonal approximation. I show that the $n$-loop result for the UV poles can be given in terms of the one-loop calculation.

The rational parts of 5-gluon one-loop amplitudes are computed by using the newly developed method for computing the rational parts directly from Feynman integrals. We found complete agreement with the previously well-known results of Bern,…

We show that the calculation of L-loop Feynman integrals in D dimensions can be reduced to a series of matrix multiplications in D times L dimensions. This gives rise to a new type of expansions for the critical exponents in three…

Two and three point functions of composite operators are analysed with regard to (logarithmically) divergent contact terms. Using the renormalisation group of dimensional regularisation it is established that the divergences are governed by…

Based on the method in Refs.~{\tt [D.~Kreimer, Z.\ Phys.\ C {\bf 54} (1992) 667} and {\tt Int.\ J.\ Mod.\ Phys.\ A {\bf 8} (1993) 1797]}, we present analytic results for scalar one-loop four-point Feynman integrals with complex internal…

We show that at one-loop order, negative-dimensional, Mellin-Barnes' (MB) and Feynman parametrization (FP) approaches to Feynman loop integrals calculations are equivalent. Starting with a generating functional, for two and then for…