Related papers: The $q \bar{q}$ relativistic interaction in the Wi…
The two-body Dirac equations for the bound q bar q systems are obtained from the different (five) versions of the 3D-equations derived from Bethe-Salpeter equation with the instantaneous kernel in the momentum space using the additional…
The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e. a map from (space-time)^N to a spin space. This concept was originally proposed by Dirac as the…
Based on the Dirac approach we have developed the relativistic vision of the WKB method for centrally symmetrical potential with mixed Lorenz structure. We have obtained relativistic wavefunctions of light quark and the new rule of…
Propagation of the heavy quark in the field of a static antiquark source is studied in the framework of effective Dirac equation. The model of QCD vacuum is described by bilocal gluonic correlators. In the heavy quark limit the effective…
The complete expression of the heavy quark-antiquark potential up to order $1/m^2$ is known from QCD in terms of Wilson loop expectation values. We use that expression and a mapping, assumed to be valid at large distances, between Wilson…
We calculate quark-antiquark potentials using the relationship between the expectation value of the Wilson loop and the action of a probe string in the string dual. We review and categorize the possible forms of the dependence of the energy…
The gravitational effects in the relativistic quantum mechanics are investigated. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. As a direct application, we analyze…
The four-dimensional Dirac-Schr\"odinger equation satisfied by quark-antiquark bound states is derived from Quantum Chromodynamics. Different from the Bethe-Salpeter equation, the equation derived is a kind of first-order differential…
We use a variational wave function to calculate the energy of the interaction between external charges in the compact Abelian gauge theory in 2+1 dimensions with mixed action. Our variational wave functions preserve the compact gauge…
The static gluon-quark-antiquark interaction is investigated using lattice QCD techniques. A Wilson loop adequate to the static hybrid three-body system is developed and, using a $24^3 \times 48$ periodic lattice with $\beta = 6.2$, the…
At the large distances compared to the chiral symmetry breaking scale, a four-quark system $\bar Q \bar Q qq$ (with $Q$ as heavy and $q$ as light quarks) can be treated as two asymptotic mesons interacting via strong residual forces. The…
In previous papers we have shown how Schr\"{o}dinger's equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field.…
The quark-antiquark bound states are discussed using the relativistic spectator (Gross) equations. A relativistic covariant framework for analyzing confined bound states is developed. The relativistic linear potential developed in an…
Relativistic formalism of Green's functions is dicussed in QCD and QED,where the relativistic Green's functions are constructed using the Schwinger proper time formalism and the Fock-Feynman-Schwinger method.As a result a simple and exact…
An equation for the quantum average of the gauge invariant Wilson loop in non-commutative Yang-Mills theory with gauge group U(N) is obtained. In the 't Hooft limit, the equation reduces to the loop equation of ordinary Yang-Mills theory.…
The bound state of constituent quarks forming a $Qqq$ composite baryon is investigated in a QCD-inspired effective light-front model. The light-front Faddeev equations are derived and solved numerically. The masses of the spin 1/2 low-lying…
A planar Maxwell-Chern-Simons-Proca model endowed with a Lorentz-violating background is taken as framework to investigate the electron-electron interaction. The Dirac sector is introduced exhibiting a Yukawa and a minimal coupling with the…
One-loop effective action of noncommutative scalar field theory with cubic self-interaction is studied. Utilizing worldline formulation, both planar and nonplanar part of the effective action are computed explicitly. We find complete…
We present the result of the quadratic-in-spin interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to NNNLO corrections within the post-Newtonian expansion. The calculation is performed by employing…
The quark sector of Coulomb gauge quantum chromodynamics is considered within the functional integral approach. The quark contributions to the Dyson-Schwinger equations are derived and one-loop perturbative results for the two-point…