Related papers: On equations of motion in twist-four evolution
QCD evolution equations can be recast in terms of parton branching processes. We present a new numerical solution of the equations. We show that this parton-branching solution can be applied to analyze infrared contributions to evolution,…
The procedure for calculation of the QCD evolution of transverse momentum dependent distributions within the covariant approach is suggested. The standard collinear QCD evolution together with the requirements of relativistic invariance and…
We illustrate the implementation of a method based on the use of recursion relations in (Bjorken) $x-$space for the solution of the evolution equations of QCD for all the leading twist distributions. The algorithm has the advantage of being…
In this Short Note we complement the intriguing harmonic analytic perspective due to P. Auscher and A. Axelsson for the abstract evolution equations. This concerns a unified approach to temporally weighted estimates for the forward and…
In the context of very general exact renormalization groups, it will be shown that, given a vertex expansion of the Wilsonian effective action, remarkable progress can be made without making any approximations. Working in QCD we will…
We show that the Collins-Soper-Sterman resummation approach to the derivation of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation is gauge invariant. The special gauge-dependent parton distribution function employed in the…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
Twisted Alexander invariants of knots are well-defined up to multiplication of units. We get rid of this multiplicative ambiguity via a combinatorial method and define normalized twisted Alexander invariants. We then show that the…
The reconnection process in the dynamics of cubic nontwist maps, introduced in [3], is studied. The present paper extends the work presented in [8]. As in that work, in order to describe the route to reconnection of the involved…
The present work pursues the aim to draw attention to unique possibilities of the skew-symmetric differential forms. At present the theory of skew-symmetric exterior differential forms that possess invariant properties has been developed.…
In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of…
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
Staple-shaped Wilson line operators are necessary for the study of transverse momentum-dependent parton distribution functions (TMDPDFs) in lattice QCD and beyond. In this work, we study the renormalization of such operators in the general…
Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two…
Quantum process tomography provides a means of measuring the evolution operator for a system at a fixed measurement time $t$. The problem of using that tomographic snapshot to predict the evolution operator at other times is generally…
An approach which unifies the Double Logarithmic Approximation at small x and the leading order DGLAP evolution of fragmentation functions at large x is presented. This approach reproduces exactly the Modified Leading Logarithm…
Consider the trilinear form for twisted convolution on $\mathbb{R}^{2d}$: \begin{equation*} \mathcal{T}_t(\mathbf{f}):=\iint f_1(x)f_2(y)f_3(x+y)e^{it\sigma(x,y)}dxdy,\end{equation*} where $\sigma$ is a symplectic form and $t$ is a…
It has been proposed that the Poincare and some other symmetries of noncommutative field theories should be twisted. Here we extend this idea to gauge transformations and find that twisted gauge symmetries close for arbitrary gauge group.…
Modified quark fragmentation functions in deeply inelastic $eA$ collisions and their QCD evolution equations are derived for the first time in the framework of multiple parton scattering. Induced radiation gives rise to additional terms in…