Related papers: Applying generalized Pad\'e approximants in analyt…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both…
A short survey of the renormalization problem in QCD and its non-perturbative solution by means of numerical simulations on the lattice is given. Most emphasis is on scale dependent renormalizations, which can be reliably addressed via a…
The perturbative QCD static potential and ultrasoft contributions, which together give the static energy, have been calculated to three- and four-loop order respectively, by several authors. Using the renormalization group, and Pad\'e…
We discuss the St\"uckelberg-Peterman extended renormalization group equations in perturbative QCD, which express the invariance of physical observables under renormalization-scale and scheme-parameter transformations. We introduce a…
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…
Precision tests of QCD perturbation theory are not readily available from experimental data. The main reasons are systematic uncertainties due to the confinement of quarks and gluons, as well as kinematical constraints which limit the…
We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories. The…
Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the ``generalized Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep inelastic…
The supersymmetric reformulation of physical observables in the Chalker-Coddington model (CC) for the plateau transition in the integer quantum Hall effect leads to a reformulation of its critical properties in terms of a 2D non-compact…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
We explain how scale dependent renormalized quantities can be computed using lattice QCD. Two examples are used: the running coupling and quark masses. A reliable computation of the $\Lambda$-parameter in the quenched approximation is…
Following Feynman's successful treatment of the polaron problem we apply the same variational principle to quenched QED in the worldline formulation. New features arise from the description of fermions by Grassmann trajectories, the…
A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale $\mu$ of the running coupling $\alpha_s(\mu^2).$ The purpose of the running coupling in any gauge theory is to sum all…
Pad'e approximants are used to improve the convergence behavior of perturbative results in massless scalar and gauge field theories at finite temperature.
We propose a method for the resummation of divergent perturbative expansions in quantum electrodynamics and related field theories. The method is based on a nonlinear sequence transformation and uses as input data only the numerical values…
A primary problem for perturbative QCD analyses is how to set the renormalization scale of the QCD running coupling in order to achieve maximally precise fixed-order predictions for physical observables. The Principle of Maximum…
We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power…
We present analytic estimates of the performances of various approximate quantum error correction schemes for the generalized amplitude damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes.…
We demonstrate the effectiveness of a generalized renormalized perturbational approach to calculate the induced magnetization for the single impurity Anderson model with a strong on-site interaction, using flow equations for renormalized…