Related papers: A Systematic Extended Iterative Solution for QCD
Self-consistent perturbation expansion up to the second order in the interaction strength is used to study a single-level quantum dot with local Coulomb repulsion attached asymmetrically to two generally different superconducting leads. At…
We construct QCD sum rules for nonperturbative studies without assuming the quark-hadron duality for the spectral density at low energy on the hadron side. Instead, both resonance and continuum contributions to the spectral density are…
Infrared safe differential cross sections, such as event shape distributions, can be measured over wide kinematic ranges, from regions where fixed order calculations are adequate to regions where nonperturbative dynamics dominate. Such…
For many nonlinear physical systems, approximate solutions are pursued by conventional perturbation theory in powers of the non-linear terms. Unfortunately, this often produces divergent asymptotic series, collectively dismissed by Abel as…
We consider procedures through which an ultraviolet cut-off regularization scheme can be modified to reproduce the same results for nonperturbative renormalized Green's functions as obtained from a dimensional regularization scheme. These…
Recent progress in the nonperturbative solution of (3+1)-dimensional Yukawa theory and quantum electrodynamics (QED) and (1+1)-dimensional super Yang-Mills (SYM) theory will be summarized. The work on Yukawa theory has been extended to…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
In this thesis, we develop resummation algorithms suitable for perturbative QCD. In the first part, we propose a resummation technique applicable to the Regge limit. We develop a new systematic procedure for this limit in perturbative QCD…
We address the long-standing problem of negative decay and production rates in perturbative QCD for exclusive processes by proposing amplitude-level NRQCD factorization as a systematic prescription. Building on this, we present the first…
By recasting the non-linear frequency-dependent $GW$ quasiparticle equation into a linear eigenvalue problem, we explain the appearance of multiple solutions and unphysical discontinuities in various physical quantities computed within the…
The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation…
A novel application of lattice QCD spectral reconstruction is presented, in which euclidean correlation function data in a fixed time range are used to infer values outside the range, enabling a model-independent investigation of the…
We develop a systematic method of the perturbative expansion around the Gaussian effective action based on the background field method. We show, by applying the method to the quantum mechanical anharmonic oscillator problem, that even the…
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…
Perturbation series for the electron propagator in the Schwinger Model is summed up in a direct way by adding contributions coming from individual Feynman diagrams. The calculation shows the complete agreement between nonperturbative and…
We apply analytic perturbation theory to the Gross--Llewellyn Smith sum rule. We study the $Q^2$ evolution and the renormalization scheme dependence of the analytic three-loop QCD correction to this sum rule, and demonstrate that the…
We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a…
Recent progress in the solution of Schwinger-Dyson equations (SDE), as well as lattice simulation of pure glue QCD, indicate that the gluon propagator and coupling constant are infrared (IR) finite. We discuss how this non-perturbative…
For $D$ a bounded domain in $\mathbb R^d, d \ge 2,$ with smooth boundary $\partial D$, the non-linear inverse problem of recovering the unknown conductivity $\gamma$ determining solutions $u=u_{\gamma, f}$ of the partial differential…
It has been shown, in the case of meson photoproduction, that the power-law falloff of these reactions can be described by lowest order (real) sum rules, at moderate momentum transfer. The phases of these processes, in this regime, are…