Related papers: Reduction of Feynman Integrals in the Parametric R…
Permutation group algebras, and their generalizations called permutation centralizer algebras (PCAs), play a central role as hidden symmetries in the combinatorics of large $N$ gauge theories and matrix models with manifest continuous gauge…
It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.
Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for constructing multivariate intersection numbers relevant to Feynman integrals,…
Using the method of uniqueness a two-loop massless propagator Feynman diagram with a non-integer index on the central line is evaluated in a very transparent way. The result is applied to the computation of the two-loop polarization…
In a recent paper we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines.…
Learning distributions over permutations is a fundamental problem in machine learning, with applications in ranking, combinatorial optimization, structured prediction, and data association. Existing methods rely on mixtures of parametric…
An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to…
We introduce a new approach for the computation of the class of Feynman integrals whose integrands vanish in strictly four-dimensions, so-called ''pseudo-evanescent'' integrals. We argue that, up to $\mathcal{O}(\epsilon)$ corrections,…
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master…
We derive parametric integral representations for the general $n$-point function of scalar operators in momentum-space conformal field theory. Recently, this was shown to be expressible as a generalised Feynman integral with the topology of…
Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that…
The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an…
We present a new computer program, $\texttt{feyntrop}$, which uses the tropical geometric approach to evaluate Feynman integrals numerically. In order to apply this approach in the physical regime, we introduce a new parametric…
We describe an algorithm to organize Feynman integrals in terms of their infrared properties. Our approach builds upon the theory of Landau singularities, which we use to classify all configurations of loop momenta that can give rise to…
A short review of the method for the tensor reduction of Feynman integrals based on recurrence relations with respect to space-time dimension d- is given. A solution of the difference equation with respect to d for the n - point one-loop…
We report on a new class of Ising Machines (IMs) that rely on coupled parametric frequency dividers (PFDs) as macroscopic artificial spins. Unlike the IM counterparts based on subharmonic injection locking (SHIL), PFD IMs do not require…
The Feynman integral for the Schroedinger propagator is constructed as a generalized function of white noise, for a linear space of potentials spanned by measures and Laplace transforms of measures, i.e., locally singular as well as rapidly…
It has been recently shown how the tensorial nature of real-time path integrals involving the Feynman-Vernon influence functional can be utilized using matrix product states, taking advantage of the finite length of the non-Markovian…
Tensor analysis has been a widely studied in physics applications including circuit theory and electric machines. This paper reviews some of the main features of this type of representation for unbalanced power distribution systems and…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…