相关论文: Non linear gluon evolution in path-integral form

We derive the complete Wilson renormalization group equation which governs the evolution of the gluon distribution and other gluonic observables at low $x$ and arbitrary density.

Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that…

Path integrals and the Wilsonian renormalization group provide two complementary computational tools for investigating continuum approaches to quantum gravity. The starting points of these constructions utilize a bare action and a fixed…

A non-Grassmanian path integral representation is given for the solution of the Klein-Gordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic…

We perform analysis of the small x non-linear evolution equation formulated in momentum space supplemented by higher order terms. The equation is defined in wide range of transverse momentum and longitudinal momentum fraction extending…

We continue the study of the effective action for low $x$ physics based on a Wilson renormalization group approach. We express the full nonlinear renormalization group equation in terms of the average value and the average fluctuation of…

For the case of reduction onto the non-zero momentum level, in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimle…

We propose an evolution equation for unintegrated gluon densities that is valid for large values of the QCD coupling constant $\bar{\alpha} _s$. Our approach is based on the linear resummation model introduced by Sta\'{s}to. We generalize…

From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular fixed point under renormalisation group evolution. We show how this picture precisely applies to their…

Analysing the asymptotic behaviour of the quark-quark elastic scattering amplitude at high energy and fixed transferred momentum and assuming that gluon is reggeized, we obtain the evolution equation for the gluon Regge trajectory in QCD.…

We consider a nonlinear evolution equation recently proposed to describe the small-$x$ hadronic physics in the regime of very high gluon density. This is a functional Fokker-Planck equation in terms of a classical random color source, which…

In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…

We propose a new evolution equation for the gluon density relevant for the region of small $x_B$. It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists…

We computed the longitudinal proton structure function $F_{L}$, using the nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-parisi (NLDGLAP) evolution equation approach at small $x$. For the gluon distribution, the nonlinear effects are related…

In this paper, we study the long time behavior of nonlinear quantum walks when the initial data is small in $l^2$. In particular, we study the case where the linear part of the quantum walk evolution operator has exactly two eigenvalues and…

We calculate quantum averages of Wilson loops (holonomies) in gauge theories on the Euclidean noncommutative plane, using a path-integral representation of the star-product. We show how the perturbative expansion emerges from a concise…

We analyze the general nonlinear evolution equations for multi gluon correlators derived in hep-ph/9709432 by restricting ourselves to a double logarithmic region. In this region our evolution equation becomes local in transverse momentum…

The running coupling constants are introduced in Quantum Mechanics and their evolution is described by the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples.…

We present a phenomenological study of the small-x behaviour of gluon distribution function $G(x,Q^2)$ at next-to-leading order (NLO) and next-to-next-to-leading order(NNLO) in light of the nonlinear Gribov-Ryskin-Levin-Mueller-Qiu…

We construct the effective Hamiltonian which governs the renormalization group flow of the gluon distribution with increasing energy and in the leading logarithmic approximation. This Hamiltonian defines a two-dimensional field theory which…