Related papers: Rational Approximations in Quantum Chromodynamics
We try to review the main current ideas and points of view on the running coupling constant in QCD. We begin by recalling briefly the classic analysis based on the Renormalization Group with some emphasis on the exact solutions of the RG…
The theory of Quantum Chromo Dynamics (QCD) reproduces the strong interaction at distances much shorter than the size of the nucleon. At larger distance scales, the generation of hadron masses and confinement cannot yet be derived from…
We compute the first perturbative correction to the static correlation lengths of light quark bilinears in hot QCD with finite quark chemical potentials. The correction is small and positive, with mu-dependence depending on the relative…
I discuss several theoretical tools which are useful for analyzing perturbative and non-perturbative problems in quantum chromodynamics, including (a) the light-cone Fock expansion, (b) the effective charge $\alpha_V$, (c) conformal…
Dynamical Coherent-Potential Approximation (CPA) to correlated electrons has been extended to a system with realistic Hamiltonian which consists of the first-principles tight-binding Linear Muffintin Orbital (LMTO) bands and intraatomic…
We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems effectively acting as their own environment. Combining a variety of concepts of quantum many-body theory, notably the…
We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes…
The two-particle problem within a nonequilibrium many-particle system is investigated in the framework of real-time Green's functions. Starting from the dynamically screened ladder approximation of the nonequlibrium Bethe-Salpeter equation,…
We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
A method of resummation of truncated perturbation series, related to diagonal Pad\'e approximants but giving results independent of the renormalization scale, was developed more than ten years ago by us with a view of applying it in…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter…
Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is accomplished…
We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on $\mathbb{Z}^d$ with certain slowly decaying long-range hopping and analytic cosine type potentials. As applications, we prove the…
We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lema\^itre-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of…
An heuristic semiclassical procedure that incorporates quantum gravity induced corrections in the description of photons and spin 1/2 fermions is reviewed. Such modifications are calculated in the framework of loop quantum gravity and they…
Standard Model determinations of properties of strongly interacting systems of hadrons have become possible with the powerful method of lattice quantum chromodynamics (LQCD), a method with growing applicability and reliability. While growth…
Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these…
We present a progress report on our investigation of the thermodynamics of QCD with $N_f=2$ flavors of dynamical Wilson fermions in the limit of a large number of colors $N_c$. To date, studies of the thermodynamics of QCD at large $N_c$…
The superconformal algebraic approach to hadronic physics is used to construct a semiclassical effective theory for nucleons which incorporates essential nonperturbative dynamical features, such as the emergence of a confining scale and the…