Related papers: Piecewise Linear Wilson lines
Wilson lines are key objects in many QCD calculations. They are parallel transporters of the gauge field that can be used to render non-local operator products gauge invariant, which is especially useful for calculations concerning…
We present an algorithm to express Wilson lines that are defined on piecewise linear paths in function of their individual segments, reducing the number of diagrams needed to be calculated. The important step lies in the observation that…
Unlike the Wilson line in QED the Wilson line in QCD contains path ordering. In this paper we get rid of the path ordering in the light-like Wilson line in QCD by simplifying all the infinite number of non-commuting terms in the SU(3) pure…
We provide a recursive diagrammatic prescription for the exponentiation of gauge theory amplitudes involving products of Wilson lines and loops. This construction generalizes the concept of webs, originally developed for eikonal form…
We discuss the divergence structure of Wilson line operators with partially overlapping segments on the basis of the cyclic Wilson loop as an explicit example. The generalized exponentiation theorem is used to show the exponentiation and…
We study hard $1\to 2$ final-state parton splittings in the medium, and put special emphasis on calculating the Wilson line correlators that appear in these calculations. As partons go through the medium their color continuously rotates, an…
A classical Wilson line is a cooresponedce between closed paths and elemets of a gauge group. However the noncommutative geometry does not have closed paths. But noncommutative geometry have good generalizations of both: the covering…
Off-lightcone Wilson-line operators are constructed using local operators connected by time-like or space-like Wilson lines, which ensure gauge invariance. Off-lightcone Wilson-line operators have broad applications in various contexts. For…
Using product integrals we review the unambiguous mathematical representation of Wilson line and Wilson loop operators, including their behavior under gauge transformations and the non-abelian Stokes theorem. Interesting consistency…
We consider the unparticle action that is made gauge invariant by inclusion of an open Wilson line factor. In deriving vertexes from such an action it has been customary to use a form of differentiating the Wilson line originally proposed…
We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of these operators as…
We show that the geometry of the Wilson lines, entering the operator definition of the transverse-momentum dependent parton distributions and that of the soft factor, follows from the kinematics of the underlying physical process in…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
A simple construction is presented, which generalises piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature,…
By using path integral formulation of QCD and QED we prove that the factorization theorem is valid for light-like Wilson line but is not valid for non-light-like Wilson line. This conclusion is shown to be consistent with Ward identity and…
Gauge fixing is an essential step in lattice QCD calculations, particularly for studying gauge-dependent observables. Traditional iterative algorithms are computationally expensive and often suffer from critical slowing down and scaling…
The Wilson loop with a wavy line contour is studied using integrable methods. The auxiliary problem is solved and the Lax operator is built to first order in perturbation theory, considering a small perturbation from the straight line.…
Wilson loops are among the most fundamental gauge-invariant observables in quantum field theory, encoding the global structure of gauge fields through their holonomy along closed contours. Originally introduced as order parameters for…
Open Wilson line operators and generalized star product have been studied extensively in noncommutative gauge theories. We show that they also show up in noncommutative scalar field theories as universal structures. We first point out that…
Several techniques were proposed to model the Piecewise linear (PWL) functions, including convex combination, incremental and multiple choice methods. Although the incremental method was proved to be very efficient, the attention of the…