Generalized Boltzmann Equation in a Manifestly Covariant Relativistic Statistical Mechanics

We consider the relativistic statistical mechanics of an ensemble of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses, to find the approximate dynamical equation for the kinetic state of any nonequilibrium system to the relativistic case, and obtain a manifestly covariant Boltzmann-type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This equation is then used to prove the $H$-theorem for evolution in $\tau .$ In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential $V(q),$ where $q$ is an invariant distance in the Minkowski space-time. The two-body correlations are taken to have the support in a relative $O( 2,1)$-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit

New Glueball-Meson Mass Relations

Using the ``glueball dominance'' picture of the mixing between q\bar{q} mesons of different hidden flavors, we establish new glueball-meson mass relations which serve as a basis for glueball spectral systematics. For the tensor glueball mass 2.3\pm 0.1 GeV used as an input parameter, these relations predict the following glueball masses: M(0^{++})\simeq 1.65\pm 0.05 GeV, M(1^{--})\simeq 3.2\pm 0.2 GeV, M(2^{-+})\simeq 2.95\pm 0.15 GeV, M(3^{--})\simeq 2.8\pm 0.15 GeV. We briefly discuss the failure of such relations for the pseudoscalar sector. Our results are consistent with (quasi)-linear Regge trajectories for glueballs with slope \simeq 0.3\pm 0.1 GeV^{-2}.Comment: Extensive revision including response to comments received, value of glueball Regge slope, and a consideration of radial excitations. 14 pages, LaTe

Gell-Mann--Okubo Mass Formula for an SU(4) Meson Hexadecuplet

Using a linear mass spectrum of an $SU(4)$ meson hexadecuplet, we derive the Gell-Mann--Okubo mass formula for the charmed mesons, in good agreement with experiment. Possible generalization of this method to a higher symmetry group is briefly discussed.Comment: 11 pages, LaTe

Towards a Realistic Equation of State of Strongly Interacting Matter

We consider a relativistic strongly interacting Bose gas. The interaction is manifested in the off-shellness of the equilibrium distribution. The equation of state that we obtain for such a gas has the properties of a realistic equation of state of strongly interacting matter, i.e., at low temperature it agrees with the one suggested by Shuryak for hadronic matter, while at high temperature it represents the equation of state of an ideal ultrarelativistic Stefan-Boltzmann gas, implying a phase transition to an effectively weakly interacting phase.Comment: LaTeX, figures not include

Effective Functional Form of Regge Trajectories

We present theoretical arguments and strong phenomenological evidence that hadronic Regge trajectories are essentially nonlinear and can be well approximated, for phenomenological purposes, by a specific square-root form.Comment: 29 pages, LaTeX. Published versio

Melting curve and phase diagram of vanadium under high-pressure and high-temperature conditions

We report a combined experimental and theoretical study of the melting curve and the structural behavior of vanadium under extreme pressure and temperature. We performed powder x-ray diffraction experiments up to 120 GPa and 4000 K, determining the phase boundary of the bcc-to-rhombohedral transition and melting temperatures at different pressures. Melting temperatures have also been established from the observation of temperature plateaus during laser heating, and the results from the density-functional theory calculations. Results obtained from our experiments and calculations are fully consistent and lead to an accurate determination of the melting curve of vanadium. These results are discussed in comparison with previous studies. The melting temperatures determined in this study are higher than those previously obtained using the speckle method, but also considerably lower than those obtained from shock-wave experiments and linear muffin-tin orbital calculations. Finally, a high-pressure high-temperature equation of state up to 120 GPa and 2800 K has also been determined

Towards resolution of the enigmas of P-wave meson spectroscopy

The mass spectrum of P-wave mesons is considered in a nonrelativistic constituent quark model. The results show the common mass degeneracy of the isovector and isodoublet states of the scalar and tensor meson nonets, and do not exclude the possibility of a similar degeneracy of the same states of the axial-vector and pseudovector nonets. Current experimental hadronic and \tau -decay data suggest, however, a different scenario leading to the a_1 meson mass \simeq 1190 MeV and the K_{1A}-K_{1B} mixing angle \simeq (37\pm 3)^o. Possible s\bar{s} states of the four nonets are also discussed.Comment: 22 pages, LaTe

Analysis of Dislocation Mechanism for Melting of Elements: Pressure Dependence

In the framework of melting as a dislocation-mediated phase transition we derive an equation for the pressure dependence of the melting temperatures of the elements valid up to pressures of order their ambient bulk moduli. Melting curves are calculated for Al, Mg, Ni, Pb, the iron group (Fe, Ru, Os), the chromium group (Cr, Mo, W), the copper group (Cu, Ag, Au), noble gases (Ne, Ar, Kr, Xe, Rn), and six actinides (Am, Cm, Np, Pa, Th, U). These calculated melting curves are in good agreement with existing data. We also discuss the apparent equivalence of our melting relation and the Lindemann criterion, and the lack of the rigorous proof of their equivalence. We show that the would-be mathematical equivalence of both formulas must manifest itself in a new relation between the Gr\"{u}neisen constant, bulk and shear moduli, and the pressure derivative of the shear modulus.Comment: 19 pages, LaTeX, 9 eps figure