Deconfinement transition for nonzero baryon density in the Field Correlator Method

Deconfinement phase transition due to disappearance of confining colorelectric field correlators is described using nonperturbative equation of state. The resulting transition temperature $T_c(\mu)$ at any chemical potential $\mu$ is expressed in terms of the change of gluonic condensate $\Delta G_2$ and absolute value of Polyakov loop $L_{fund} (T_c)$, known from lattice and analytic data, and is in good agreement with lattice data for $\Delta G_2 \approx 0.0035$ GeV$^4$. E.g. $T_c(0) =0.27; 0.19; 0.17$ GeV for $n_f=0,2,3$ respectively.Comment: 8 pages, 1 figure, LaTeX2e; some typos correcte

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

Analytic calculation of field-strength correlators

Field correlators are expressed using background field formalism through the gluelump Green's functions. The latter are obtained in the path integral and Hamiltonian formalism. As a result behaviour of field correlators is obtained at small and large distances both for perturbative and nonperturbative parts. The latter decay exponentially at large distances and are finite at x=0, in agreement with OPE and lattice data.Comment: 28 pages, no figures; new material added, misprints correcte

Decay constants of the heavy-light mesons from the field correlator method

Meson Green's functions and decay constants $f_{\Gamma}$ in different channels $\Gamma$ are calculated using the Field Correlator Method. Both, spectrum and $f_\Gamma$, appear to be expressed only through universal constants: the string tension $\sigma$, $\alpha_s$, and the pole quark masses. For the $S$-wave states the calculated masses agree with the experimental numbers within $\pm 5$ MeV. For the $D$ and $D_s$ mesons the values of $f_{\rm P} (1S)$ are equal to 210(10) and 260(10) MeV, respectively, and their ratio $f_{D_s}/f_D$=1.24(3) agrees with recent CLEO experiment. The values $f_{\rm P}(1S)=182, 216, 438$ MeV are obtained for the $B$, $B_s$, and $B_c$ mesons with the ratio $f_{B_s}/f_B$=1.19(2) and $f_D/f_B$=1.14(2). The decay constants $f_{\rm P}(2S)$ for the first radial excitations as well as the decay constants $f_{\rm V}(1S)$ in the vector channel are also calculated. The difference of about 20% between $f_{D_s}$ and $f_D$, $f_{B_s}$ and $f_B$ directly follows from our analytical formulas.Comment: 37 pages, 10 tables, RevTeX

Dynamics of confined gluons

Propagation of gluons in the confining vacuum is studied in the framework of the background perturbation theory, where nonperturbative background contains confining correlators. Two settings of the problem are considered. In the first the confined gluon is evolving in time together with static quark and antiquark forming the one-gluon static hybrid. The hybrid spectrum is calculated in terms of string tension and is in agreement with earlier analytic and lattice calculations. In the second setting the confined gluon is exchanged between quarks and the gluon Green's function is calculated, giving rise to the Coulomb potential modified at large distances. The resulting screening radius of 0.5 fm presents a serious problem when confronting with lattice and experimental data. A possible solution of this discrepancy is discussed.Comment: 17 pages, no figures; v2: minor numerical changes in the tabl

Induced quantum numbers of a magnetic monopole at finite temperature

A Dirac electron field is quantized in the background of a Dirac magnetic monopole, and the phenomenon of induced quantum numbers in this system is analyzed. We show that, in addition to electric charge, also squares of orbital angular momentum, spin, and total angular momentum are induced. The functional dependence of these quantities on the temperature and the CP-violating vacuum angle is determined. Thermal quadratic fluctuations of charge and squared total angular momentum, as well as the correlation between them and their correlations with squared orbital angular momentum and squared spin, are examined. We find the conditions when charge and squared total angular momentum at zero temperature are sharp quantum observables rather than mere quantum averages.Comment: 24 pages, minor grammatical changes, journal versio

Multidimensional Dynamical Systems Accepting the Normal Shift

The dynamical systems of the form \ddot\bold r=\bold F (\bold r,\dot\bold r) in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force field \bold F(\bold r,\dot\bold r) of the dynamical systems with weak and complete normality are derived.Comment: AMS-TeX, ver. 2.1, IBM AT-386, size 16K (ASCII), short versio