Related papers: Non linear gluon evolution in path-integral form
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the…
Dominant present path for determination of quarks and gluon distribution functions from data is based on pre-assumed form of parameters. Here, an alternative direct, or non-parametric method is spelled out. As the main task, least square…
We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal…
In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it…
Unitary and dissipative models of quantum dynamics are linear maps on the space of states or density matrices. This linearity encodes the superposition principle, a key feature of quantum theory. However, this principle can break down in…
In the high energy limit of hadron collisions, the evolution of the gluon density in the longitudinal momentum fraction can be deduced from the Balitsky hierarchy of equations or, equivalently, from the nonlinear…
The method of the factorization of the path integral measure, based on a nonlinear filtering equation, is extended to the case of a nonfree isometric action of the compact semisimple unimodular Lie group on a smooth compact Riemannian…
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
In this paper we present solutions of evolution equations for inclusive distribution of gluons as produced by jet traversing quark-gluon plasma. We reformulate the original equations in such a form that the virtual and unresolved-real…
We discuss the structure and main features of the nonlinear evolution equation proposed by this author as the fundamental dynamical law within the framework of Quantum Thermodynamics. The nonlinear equation generates a dynamical group…
We theoretically study the geometric effect of quantum dynamical evolution in the presence of a nonequilibrium noisy environment. We derive the expression of the time dependent geometric phase in terms of the dynamical evolution and the…
We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
Algebraic random walks (ARW) and quantum mechanical random walks (QRW) are investigated and related. Based on minimal data provided by the underlying bialgebras of functions defined on e. g the real line R, the abelian finite group Z_N, and…
We study the stochastic quantization of two-dimensional nonlinear sigma model in the large $N$ limit. Our main tool is the {\it effective} Langevin equation with which we investigate nonperturbative phenomena and derive the results which…
A manifestly gauge invariant continuous renormalization group flow equation is constructed for pure SU(N) gauge theory. The formulation makes sense without gauge fixing and manifestly gauge invariant calculations may thus be carried out.…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
The nonlinear generalization of the von Neumann equation preserving convexity of the state space is studied in the nontrivial case of the qutrit. This equation can be cast into the integrable classical Riccati system of nonlinear ordinary…
Renormalization Group Equations in integro-differential form describing the evolution of cascades or resumming logarithmic scaling violations have been known in quantum field theory for a long time. These equations have been traditionally…