Related papers: Power Divergences in Overlapping Wilson Lines
By recent work of the author, Wilson's theorem as well as the Wilson quotient can be described by supercongruences of power sums of Fermat quotients modulo every higher prime power. We translate these congruences into congruences of power…
We consider both finite and infinite power chi expansions of $f$-divergences derived from Taylor's expansions of smooth generators, and elaborate on cases where these expansions yield closed-form formula, bounded approximations, or analytic…
We use an s-channel picture of hard hadronic collisions to investigate the parton distribution function for quarks at small momentum fraction x, which corresponds to very high energy scattering. We study the renormalized quark distribution…
We provide the solution to the normal ordering problem for powers and exponentials of two classes of operators. The first one consists of boson strings and more generally homogeneous polynomials, while the second one treats operators linear…
Wilson loops in gauge theories pose a fundamental challenge for dualities. Wilson loops are labeled by a representation of the gauge group and should map under duality to loop operators labeled by the same data, yet generically, dual…
The Lambert W function gives the solutions of a simple exponential polynomial. The generalized Lambert W function was defined by Mez\"{o} and Baricz, and has found applications in delay differential equations and physics. In this article we…
We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a…
We discuss the relation between the infrared singularities of on-shell partonic form factors and parton distribution functions (PDFs) near the elastic limit, through their factorisation in terms of Wilson-line correlators. Ultimately we…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
A phenomenological analysis of the distribution of Wilson loops in SU(2) Yang-Mills theory is presented in which Wilson loop distributions are described as the result of a diffusion process on the group manifold. It is shown that, in the…
We study the divergences of Wilson loops for a contour with a cusp of zero opening angle, combined with a nonzero discontinuity of its curvature. The analysis is performed in lowest order, both for weak and strong coupling. Such a spike…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
We study contact interactions for long world-lines on a curved surface, focusing on the average number of times two world-lines intersect as a function of their end-points. The result can be used to extend the concept of path-ordering, as…
In this article, we prove a representation theorem that any generic line arrangement in the plane over an ordered field which has global cyclicity can be represented isomorphically by a line arrangement with a given set of distinct slopes…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We develop a theory of extrapolation for weights that satisfy a generalized reverse H\"older inequality in the scale of Orlicz spaces. This extends previous results by Auscher and Martell [2] on limited range extrapolation. As an…
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…
We consider the coordinate-space matrix elements that correspond to fixed-angle scattering amplitudes involving partons and Wilson lines in coordinate space, working in Feynman gauge. In coordinate space, both collinear and short-distance…
The leading singularities of one-loop scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory are known to factorise into products of tree-level amplitudes, and this can be seen from a number of different perspectives e.g.…
The Law of the Iterated Logarithm for some Markov operators, which converge exponentially to the invariant measure, is established. The operators correspond to iterated function systems which, for example, may be used to generalize the cell…