Related papers: Analytic Invariant Charge in QCD
Recalling that the rotating wave approximation (RWA) is only valid in the weak coupling regimes, the purpose of this paper is to study the Hamiltonian dynamics describing the full quantum mechanical approach of the interaction between…
For the first time, physicists are in the position to precisely study a fully relativistic quantum field theory: Quantum ChromoDynamics (QCD). QCD is a central element of the Standard Model and provides the theoretical framework for…
These lecture notes focus on the bound state sector of QCD. Motivated by data which suggests that the strong coupling \alpha_s(Q) freezes at low Q, and by similarities between the spectra of hadrons and atoms, I discuss if and how QCD bound…
We discuss the model $\bar{\alpha}_{an}(Q^2)$ recently proposed for the QCD running coupling $\bar{\alpha}_s(Q^2)$ in the Euclidean domain on the basis of the "asymptotic-freedom" expression and on causality condition in the form of the…
The standard model of strong interactions invokes the quantum chromodynamics (QCD) of quarks and gluons interacting within a fluid. At sufficiently small length scales, the effective interactions between the color charged particles within…
We present a new approach to determining the strong coupling $\alpha_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $\Lambda_{\mathrm{QCD}}$ and up to the Planck scale $\sim1.22\cdot10^{19}$\,GeV, with the…
We present a full introduction to the recent devised perturbation theory for strong coupling in quantum mechanics. In order to put the theory in a proper historical perspective, the approach devised in quantum field theory is rapidly…
In the framework of analytic approach to QCD, which has been recently intensively developed, the dependence of nonperturbative contributions in a running coupling of strong interaction on initial perturbative approximation to 3-loop order…
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
Nonrelativistic bound states are studied using an effective field theory. Large logarithms in the effective theory can be summed using the velocity renormalization group. For QED, one can determine the structure of the leading and…
The renormalization group (RG) approach is largely responsible for the considerable success which has been achieved in developing a quantitative theory of phase transitions. This work treats the rigorous definition of the RG map for…
The renormalization of the effective field theories (EFTs) in many-body systems is the most pressing and challenging problem in modern nuclear ab initio calculation. For general non-relativistic EFTs, we prove that the renormalization group…
A new application of the density matrix renormalization group (DMRG) method to a system composed of an interacting dot coupled to a infinite one dimensional lead is presented. This method enables one to study the influence of the coupling…
We calculate the spin and charge dynamical susceptibilities of a strongly correlated impurity model in a renormalised perturbation theory. The irreducible for vertices for the quasiparticle scattering are deduced from the renormalised…
The analytization procedure which allows one to remove nonphysical singularities of the QCD running coupling constant $\bar\alpha_s(q^2)$ in the infrared region is applied to standard as well as to iterative solutions of the two-loop…
We describe here the coherent formulation of electromagnetism in the non-relativistic quantum-mechanical many-body theory of interacting charged particles. We use the mathematical frame of the field theory and its quantization in the spirit…
Nonperturbative studies of the strong running coupling constant in the infrared region are discussed. Starting from the analyses of the Dyson -- Schwinger equations in the gauge sector of QCD, the conclusion is made on an incomplete fixing…
We discuss how to implement the source terms in Quantum Chromodynamics (QCD) respecting gauge invariance and noncommutativity of color charge density operators. We start with decomposing the generating functional of QCD into constituents…
We construct some AdS/QCD models by the systematic procedure of GKN. These models reflect three rather different asymptotics the gauge theory beta functions approach at the infrared region, $\beta\propto-\lambda^2, -\lambda^3$ and…
Based on a study of the analytic running coupling obtained from the standard perturbation theory results up to four-loop order, the QCD ``synthetic'' running coupling \alpha_{syn} is built. In so doing the perturbative time-like…