The matrix Hamiltonian for hadrons and the role of negative-energy components

The world-line (Fock-Feynman-Schwinger) representation is used for quarks in arbitrary (vacuum and valence gluon) field to construct the relativistic Hamiltonian. After averaging the Green's function of the white $q\bar q$ system over gluon fields one obtains the relativistic Hamiltonian, which is matrix in spin indices and contains both positive and negative quark energies. The role of the latter is studied in the example of the heavy-light meson and the standard einbein technic is extended to the case of the matrix Hamiltonian. Comparison with the Dirac equation shows a good agreement of the results. For arbitrary $q\bar q$ system the nondiagonal matrix Hamiltonian components are calculated through hyperfine interaction terms. A general discussion of the role of negative energy components is given in conclusion.Comment: 29 pages, no figure

Curvature Expansion for the Gluodynamics String including Perturbative Gluonic Contributions

Perturbation theory in the nonperturbative QCD vacuum and the non-Abelian Stokes theorem, representing a Wilson loop in the SU(2) gluodynamics as an integral over all the orientations in colour space, are applied to a derivation of the correction to the string effective action in the lowest order in the coupling constant $g$. This correction is due to the interaction of perturbative gluons with the string world sheet and affects only the coupling constant of the rigidity term, while its contribution to the string tension of the Nambu-Goto term vanishes. The obtained correction to the rigidity coupling constant multiplicatively depends on the colour "spin" of the representation of the Wilson loop under consideration and a certain path integral, which includes the background Wilson loop average.Comment: 9 pages, LaTeX, no figure

Mesons in ultra-intense magnetic field: an evaded collapse

Spectra of $q \bar q$ mesons are investigated in the framework of the Hamiltonian obtained from the relativistic path integral in external homogeneous magnetic field. The spectra of all 12 spin-isospin s-wave states generated by $\pi$- and $\rho$-mesons with different spin projections, are studied analytically as functions of the field strength. Three types of behavior with characteristic splittings are found. The results are in agreement with recent lattice calculations.Comment: 7 pages, 5 figures, XIIth Quark Confinement and the Hadron Spectrum, 28 Aug. - 4 Sep. 201

Light meson radial Regge trajectories

A new physical mechanism is suggested to explain the universal depletion of high meson excitations. It takes into account the appearance of holes inside the string world sheet due to $q\bar{q}$ pair creation when the length of the string exceeds the critical value $R_1 \simeq 1.4$ fm. It is argued that a delicate balance between large $N_c$ loop suppression and a favorable gain in the action, produced by holes, creates a new metastable (predecay) stage with a renormalized string tension which now depends on the separation r. This results in smaller values of the slope of the radial Regge trajectories, in good agreement with the analysis of experimental data in [Ref.3]Comment: 25 pages, 1 figur

Gluonic correlation length from spin-dependent potentials

The vacuum gluonic correlation length is extracted from recent lattice data on spin-dependent interquark potentials in heavy quarkonia. It is shown that the data are consistent with extremely small values of the correlation length, Tg<0.1 fm.Comment: LaTeX2e, 6 pages, uses jetpl.cls (included), version to appear in JETP Let