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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., Comment: 20 pages, 5 figures

The phase diagram of Zn has been explored up to 140 GPa and 6000 K, by combining optical observations, x-ray diffraction, and ab-initio calculations. In the pressure range covered by this study, Zn is found to retain a hexagonal close-packed crystal symmetry up to the melting temperature. The known decrease of the axial ratio of the hcp phase of Zn under compression is observed in x-ray diffraction experiments from 300 K up to the melting temperature. The pressure at which the axial ratio reaches the square root of 3 value, around 10 GPa, is slightly affected by temperature. When this axial ratio is reached, we observed that single crystals of Zn, formed at high temperature, break into multiple polycrystals. In addition, a noticeable change in the pressure dependence of the axial ratio takes place at the same pressure. Both phenomena could be caused by an isomorphic second-order phase transition induced by pressure in Zn. The reported melt curve extends previous results from 24 to 135 GPa. The pressure dependence obtained for the melting temperature is accurately described up to 135 GPa by using a Simon-Glatzel equation. The determined melt curve agrees with previous low-pressure studies and with shock-wave experiments, with a melting temperature of 5060 K at 135 GPa. Finally, a thermal equation of state is reported, which at room-temperature agrees with the literature., Comment: 26 pages, 7 figures

We apply a phenomenological approach based on nonlinear Regge trajectories to glueball states. The parameters, i.e., intercept and threshold, or trajectory termination point beyond which no bound states should exist, are determined from pomeron (scattering) data. Systematic errors inherent to the approach are discussed. We then predict masses of glueballs on the tensor trajectory. For comparison, the approach is applied to available quenched lattice data. We find a discrepancy between the lattice based thresholds and the pomeron threshold that we extract from data., Comment: 15pp., revtex4, 2 figs

The microscopic mechanism of the melting of a crystal is analyzed by the constant pressure Monte Carlo simulation of a Lennard-Jones fcc system. Beyond a temperature of the order of 0.8 of the melting temperature, we found that the relevant excitations are lines of defects. Each of these lines has the structure of a random walk of various lengths on an fcc defect lattice. We identify these lines with the dislocation ones proposed in recent phenomenological theories of melting. Near melting we find the appearance of long lines that cross the whole system. We suggest that these long lines are the precursor of the melting process., Comment: 5 pages, 5 figures, accepted in Physical Review Letters

An analytic model of the shear modulus applicable at temperatures up to melt and at all densities is presented. It is based in part on a relation between the melting temperature and the shear modulus at melt. Experimental data on argon are shown to agree with this relation to within 1%. The model of the shear modulus involves seven parameters, all of which can be determined from zero-pressure experimental data. We obtain the values of these parameters for 11 elemental solids. Both the experimental data on the room-temperature shear modulus of argon to compressions of \sim 2.5, and theoretical calculations of the zero-temperature shear modulus of aluminum to compressions of \sim 3.5 are in good agreement with the model. Electronic structure calculations of the shear moduli of copper and gold to compressions of 2, performed by us, agree with the model to within uncertainties., Comment: 20 pages, LaTeX, 9 eps figures; changes in the text

We model the density dependence of the Gruneisen parameter as gamma(rho) = 1/2 + gamma_1/rho^{1/3} + gamma_2/rho^{q}, where gamma_1, gamma_2, and q>1 are constants. This form is based on the assumption that gamma is an analytic function of V^{1/3}, and was designed to accurately represent the experimentally determined low-pressure behavior of gamma. The numerical values of the constants are obtained for 20 elemental solids. Using the Lindemann criterion with our model for gamma, we calculate the melting curves for Al, Ar, Ni, Pd, and Pt and compare them to available experimental melt data. We also determine the Z (atomic number) dependence of gamma_1. The high-compression limit of the model is shown to follow from a generalization of the Slater, Dugdale-MacDonald, and Vashchenko-Zubarev forms for the dependence of the Gruneisen parameter., Comment: 14 Pages, LaTeX, 5 eps figues; changes in the text

Regge trajectories of quark-antiquark mesons can be well approximated for phenomenology purposes by a specific nonlinear form, reflecting that the flux tubes cannot be arbitrarily large, but break due to the effect of pair-production. If confirmed, this would imply that there is only a finite number of bound states on each trajectory, and consequently, an existence of ``spectroscopy windows'' for each flavor. Here we present our results for these windows., Comment: talk presented by MB at Quark Confinement and Hadron Spectrum IV, Vienna, July 2000. To appear in the procceedings, requires sprocl.sty. 3 pages, 1 ps figure

Meson spectra can be well approximated by a specific form of a nonlinear Regge trajectory which is consistent with a finite number of bound states. This may have important consequencies for experiment, and may be a hint for the theory., Comment: talk presented by MB at the Light-Cone Meeting in Heidelberg, June 2000. To appear in the proceedings, requires elsart.cls. 4 pages

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 version

We present a new generalized string model for Regge trajectories J=J(E^2), where J and E are the orbital momentum and energy of the string, respectively. We demonstrate that this model is not to produce linear Regge trajectories, in contrast to the standard Nambu-Goto string, but generally nonlinear trajectories, which in many cases can be given in analytic form. As an example, we show how the model generates square-root, logarithmic and hyperbolic trajectories that have been discussed in the literature., Comment: 11 pages, LaTeX

Using an unquenched lattice potential to calculate the spectrum of the bottomonium system, we demonstrate numerically that the effect of pair creation is to produce termination of hadronic Regge trajectories, in contrast to the Veneziano model and the vast majority of phenomenological generalizations. Termination of Regge trajectories may have significant experimental consequences., Comment: 8 pages, 3 figures, published version including a discussion of coupling to open channels

We study the origins of the inaccuracies of Schwinger's nonet mass, and the Sakurai mass-mixing angle, formulae for the pseudoscalar meson nonet, and suggest new versions of them, modified by the inclusion of the pseudoscalar decay constants. We use these new formulae to determine the pseudoscalar decay constants and mixing angle. The results obtained, $f_8/f_\pi = 1.185\pm 0.040,$ $f_9/f_\pi =1.095\pm 0.020,$ $f_\eta /f_\pi = 1.085\pm 0.025,$ $f_{\eta ^{'}}/f_\pi =1.195\pm 0.035,$ $\theta = (-21.4\pm 1.0)^o,$ are in excellent agreement with experiment., Comment: 12 pages, LaTeX. Shortened version of hep-ph/9802404 published in Physics Letters B 427 (1998) 361

We show that Regge trajectories for all flavors suggested recently by Filipponi et al. cannot combine both meson spectroscopy and additivity of intercepts. Other defects of these trajectories are also discussed., Comment: 2 pages, LaTeX

We show that linear Regge trajectories for mesons and baryons, and the cubic mass spectrum associated with them, determine expressions for the hadron masses in terms of the universal Regge slope \alpha' alone. The ground state hadron masses as calculated from these expressions are in excellent agreement with experiment for \alpha'=0.85 GeV^{-2}., Comment: 7 pages, LaTeX. Presented at the PRQT '98 Conference, Houston, Texas, Feb 9-11, 1998

We show that Regge phenomenology is consistent with the only universal scaling law for hadron masses, M^\ast /M=(\alpha ^{'}/\alpha ^{'\ast})^{1/2}, where asterisk indicates a finite-temperature quantity. Phenomenological models further suggest the following expression of the above scaling in terms of the temperature-dependent gluon condensate: M^\ast / M = (\alpha^'/\alpha^{'\ast})^{1/2} = (^\ast/)^{1/4}., Comment: 6 pages, LaTeX. Presented at the PRQT '98 Conference, Houston, Texas, Feb 9-11, 1998

We show that linear Regge trajectories for mesons and glueballs, and the cubic mass spectrum associated with them, determine a relation between the masses of the \rho meson and the scalar glueball, M(0^{++})=3/\sqrt{2} M(\rho ), which implies M(0^{++})=1620\pm 10 MeV. We also discuss relations between the masses of the scalar and tensor and 3^{--} glueballs, M(2^{++})=\sqrt{2} M(0^{++}), M(3^{--})=2M(0^{++}), which imply M(2^{++})=2290\pm 15 MeV, M(3^{++})=3240\pm 20 MeV., Comment: 8 pages, LaTeX. Contribution to the PRQT '98 Conference, Houston, Texas, Feb 9-11, 1998

We study the origins of the inaccuracies of Schwinger's nonet mass, and the Sakurai mass-mixing angle, formulae for the pseudoscalar meson nonet, and suggest new versions of them, modified by the inclusion of the pseudoscalar decay constants. We use these new formulae to determine the pseudoscalar decay constants and mixing angle. The results obtained, f_8/f_\pi =1.185\pm 0.040, f_9/f_\pi =1.095\pm 0.020, f_\eta /f_\pi =1.085\pm 0.025, f_{\eta ^{'}}/f_\pi =1.195\pm 0.035, \theta =(-21.4\pm 1.0)^o, are in excellent agreement with experiment., Comment: 17 pages, LaTeX

We show that only additivity of inverse Regge slopes is consistent with both the formal chiral limit m(n)\to 0 and the heavy quark limit M(Q)>>M(n), where n=u,d, and m,M are current and constituent quark masses, respectively., Comment: 11 pages, LaTeX

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, LaTeX

We prove the validity of Schwinger's quartic nonet mass formula for a general nonet structure with the isoscalar singlet mass being shifted from its ``ideal'' value. We apply this formula to the problem of the correct q\bar{q} assignment for the scalar meson nonet. The results favor scalar isoscalar singlet and isoscalar octet masses in the vicinity of 1 GeV and 1.45 GeV, respectively. We explain the failure of Schwinger's formula for the pseudoscalar meson nonet, and suggest a new version of this formula, modified by the inclusion of the pseudoscalar decay constants, which holds with improved accuracy for this nonet. We also rederive the new Gell-Mann-Okubo mass formula 3M^2(n\bar{n},I=1)+2M^2(s\bar{s})=4M^2(s\bar{n})+M^2(n\bar{n},I=0) (n=u,d), suggested in our previous publications., Comment: 11 pages, LaTeX

We rederive the new SU(3) multiplet mass formula 2M^2(s\bar{s})+3M^2(n\bar{n}, I=1)=4M^2(s\bar{n})+M^2(n\bar{n},I=0) (n=u,d}, obtained in our previous paper by using Regge phenomenology, for the pseudoscalar and scalar mesons in the Nambu-Jona-Lasinio model with instanton-induced interaction. We apply this formula to the problem of the correct q\bar{q} assignment for the scalar meson nonet. Our results strongly favor the masses of the scalar isoscalar mostly octet and mostly singlet states in the vicinity of 1.45 GeV and 1.1 GeV, respectively, Comment: 15 pages, LaTeX

We show that the application of Regge phenomenology to SU(4) meson multiplets leads to a new Gell-Mann-Okubo mass-mixing formula in the SU(3) sector, 3m_1^2 + (cos theta)^2 m_0^2 + (sin theta)^2 m_{0'}^2 + sqrt{2} sin(2theta) (m_0^2 - m_{0'}^2) = 4m_{1/2}^2, where m_1,m_{1/2},m_0,m_{0'} are the masses of the isovector, isodoublet, isoscalar mostly octet and isoscalar mostly singlet states, respectively, and theta is the nonet mixing angle. For an ideally mixed nonet, theta = arctan(1/sqrt{2}), this formula reduces to 2m_0^2 + 3m_1^2 = 4m_{1/2}^2 + m_{0'}^2 which holds with an accuracy of ~1% for vector and tensor mesons. For pseudoscalar mesons, with the eta-eta' mixing angle -arctan[1/(2sqrt{2})] ~ -19.5^o, in agreement with experiment, it leads to the relation 4m_K^2 = 3m_pi^2 + m_{eta'}^2 which holds to an accuracy of better than 1% for the measured pseudoscalar meson masses., Comment: 11 pages, LaTeX

By assuming the existence of (quasi)-linear Regge trajectories for heavy mesons, we derive new quadratic mass relations of non-Gell-Mann-Okubo type, 6M^2(q-qbar)+3M^2(c-cbar)=8M^2(c-qbar), 20M^2(q-qbar)+5M^2(b-bbar)= 16M^2(b-qbar), q=n(=u,d),s, which show excellent agreement with experiment. We also establish the sum rule M^2(i-ibar)+M^2(j-jbar)-2M^2(j-ibar)\approx const for any pair of flavors, (i,j)., Comment: 17 pages, LaTeX

By assuming the existence of (quasi)-linear baryon Regge trajectories, we derive new quadratic Gell-Mann-Okubo type baryon mass relations. These relations are used to predict the masses of the charmed baryons absent from the Baryon Summary Table so far, in good agreement with the predictions of many other approaches., Comment: 14 pages, LaTeX

By assuming the existence of (quasi)-linear Regge trajectories for heavy quarkonia in the low energy region, we derive a new, sixth power, meson mass relation which shows good agreement with experiment for both charmed and beauty mesons. This relation may be reduced to a quadratic Gell-Mann-Okubo type formula by fitting the values of the Regge slopes of these (quasi)-linear trajectories. For charmed mesons, such a formula holds with an accuracy of $\sim 1$%, and is in qualitative agreement with the relation obtained previously by the application of the linear spectrum to a meson hexadecuplet., Comment: 10 pages, LaTeX

By assuming the existence of (quasi)-linear Regge trajectories for 25-plet mesons in the low energy region, we derive a new, 14th power, meson mass relation. This relation may be reduced to a quadratic Gell-Mann-Okubo type formula by fitting the values of the Regge slopes of these (quasi)-linear trajectories. Such a formula holds with an accuracy of ~2% for vector mesons, and also suggests that the quantum number I(J^P)=1/2(2^{+}) should be assigned to the both B_J(5732) and B_{sJ}(5850) mesons discovered recently. We also discuss reasons for the failure of group theory to produce correct mass relations for heavy quarkonia., Comment: 11 pages, LaTeX

The mass spectrum of D-wave mesons is considered in a nonrelativistic constituent quark model. The results show a common mass degeneracy of the isovector and isodoublet states of the 1 $^3D_1$ and 1 $^3D_3$ nonets, and suggest therefore that the $K^\ast (1680)$ cannot be the I=1/2 member of the 1 $^3D_1$ nonet. They also suggest that the $\eta _2(1870),$ presently omitted form the Meson Summary Table, should be interpreted as the I=0 $s\bar{s}$ state of the 1 $^1D_2$ nonet., Comment: 11 pages, LaTeX

By the application of a linear mass spectrum to a composite system of both the pseudoscalar and scalar meson nonets, we find three mass relations for the masses of the scalar states which suggest the $q\bar{q}$ assignment for the scalar meson nonet: $a_0(1320),$ $K_0^\ast (1430),$ $f_0(1500),$ $f_0'(980).$, Comment: 16 pages, LaTeX

In a nonrelativistic constituent quark model we find a constraint on the mixing angle of the strange axial-vector mesons, $35^o\stackrel{<}{\sim } \theta _K\stackrel{<}{\sim }55^o,$ determined solely by two parameters: the mass difference of the $a_1$ and $b_1$ mesons and the ratio of the constituent quark masses., Comment: 8 pages, LaTeX

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, LaTeX

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, LaTeX

The formulas for the temperature dependences of the non-strange and strange quark condensates are derived by taking into account the contribution of the massive resonances. Critical temperature of the chiral symmetry restoration transition is established to be 190 MeV if only meson resonances are considered, and 175 MeV if both meson and baryon resonances are taken into account., Comment: 16 pages, LaTeX, 2 postscript figures

It is argued that the mass spectrum of a meson nonet is linear, consistent with the standard Gell-Mann--Okubo mass formula and leading to an extra Gell-Mann--Okubo mass relation for the masses of the isoscalar states. This relation is shown to hold with an accuracy of up to $\sim $3\% for all well-established nonets. It also suggests a new $q\bar{q}$ assignment for the scalar meson nonet., Comment: 11 pages, LaTeX, 4 postscript figures following the main text

It is argued that the mass spectrum of a baryon octet is linear, consistent with a Gell-Mann--Okubo type relation for the squared masses of the baryons obtained previously by Bal\'{a}zs and Nicolescu. The mass spectrum of a baryon decuplet is briefly discussed., Comment: 9 pages, LaTeX, 4 postscript figures

In the model of a first order quark-gluon/hadron phase transition in which the hadronic phase is considered as vacuum bubbles growing in the quark-gluon background with chiral symmetry broken inside the bubble, we find the estimate for the length scale associated with inhomogeneities originated during the transition, $10$ m $\;\stackrel{<}{\sim }\ell \stackrel{<}{\sim }40$ m, being sufficient to produce significant effects on cosmological nucleosynthesis., Comment: 10 pages, LaTeX, to appear in Phys. Lett. B, 1996

The equation of state of hot hadronic matter is obtained, by taking into account the contribution of the massive states with the help of the resonance spectrum $\tau (m)\sim m^3$ justified by the authors in previous papers. This equation of state is in agreement with that provided by the low-temperature expansion for the pion intracting gas. It is shown that in this picture the deconfinement phase transition is absent, in agreement with lattice gauge calculations which show the only phase transition of chiral symmetry restoration. The latter is modelled with the help of the restriction of the number of the effective degrees of freedom in the hadron phase to that of the microscopic degrees of freedom in the quark-gluon phase, through the corresponding truncation of the hadronic resonance spectrum, and the decrease of the effective hadron masses with temperature, predicted by Brown and Rho. The results are in agreement with lattice gauge data and show a smooth crossover in the thermodynamic variables in a temperature range $\sim 50$ MeV., Comment: 21 pages, LaTeX, 3 postscript figures

The identification of problematic meson states as the members of the quark model $q\bar{q}$ nonets by using a hadronic resonance spectrum is discussed. The results favor the currently adopted $q\bar{q}$ assignments for the axial-vector, tensor, and 1 $^3F_4$ $J^{PC}=4^{++}$ meson nonets, and suggest a new $q\bar{q}$ assignment for the scalar meson nonet which favors the interpretation of the $f_0(980)$ and $f_0(1710)$ mesons as non-$q\bar{q}$ objects. We also suggest that the 2 $^3S_1$ $\frac{1}{2}(1^{-})$ state should be identified with the $K^\ast (1680)$ rather than $K^\ast (1410)$ meson., Comment: Latex, 13 pages plus 8 figures

We prove the uncertainty relation $T_{\triangle V}\triangle m\stackrel{>}{\sim }2\pi \hbar /c^2,$ which is realized on a statistical mechanical level for an ensemble of events in $(1+D)$-dimensional spacetime with motion parametrized by an invariant ``proper time'' $\tau ,$ where $T_{\triangle V}$ is the average passage interval in $\tau $ for the events which pass through a small (typical) $(1+D)$-volume $\triangle V,$ and $\triangle m$ is the dispersion of mass around its on-shell value in such an ensemble. We show that a linear mass spectrum is a completely general property of a $(1+D)$-dimensional off-shell theory., Comment: Latex, 13 pages

We discuss the properties of an ideal relativistic gas of events possessing Bose-Einstein statistics. We find that the mass spectrum of such a system is bounded by $\mu \leq m\leq 2M/\mu _K,$ where $\mu $ is the usual chemical potential, $M$ is an intrinsic dimensional scale parameter for the motion of an event in space-time, and $\mu _K$ is an additional mass potential of the ensemble. For the system including both particles and antiparticles, with nonzero chemical potential $\mu ,$ the mass spectrum is shown to be bounded by $|\mu |\leq m\leq 2M/\mu _K,$ and a special type of high-temperature Bose-Einstein condensation can occur. We study this Bose-Einstein condensation, and show that it corresponds to a phase transition from the sector of continuous relativistic mass distributions to a sector in which the boson mass distribution becomes sharp at a definite mass $M/\mu _K.$ This phenomenon provides a mechanism for the mass distribution of the particles to be sharp at some definite value., Comment: Latex, 22 pages

We consider 5D Kaluza-Klein type cosmological model with the fifth coordinate being a generalization of the invariant ``historical'' time $\tau $ of the covariant theory of Horwitz and Piron. We distinguish between vacuum-, off-shell matter-, and on-shell matter-dominated eras as the solutions of the corresponding 5D gravitational field equations, and build an inflationary scenario according to which passage from the off-shell matter-dominated era to the on-shell one occurs, probably as a phase transition. We study the effect of this phase transition on the expansion rate in both cases of local $O(4,1)$ and $O(3,2)$ invariance of the extended $(x^\mu ,\tau )$ manifold and show that it does not change in either case. The expansion of the model we consider is not adiabatic; the thermodynamic entropy is a growing function of cosmic time for the closed universe, and can be a growing function of historical time for the open and the flat universe. A complete solution of the 5D gravitational field equations is obtained for the on-shell matter-dominated universe. The open and the closed universe are shown to tend asymptotically to the standard 4D cosmological models, in contrast to the flat universe which does not have the corresponding limit. Finally, possible cosmological implications are briefly discussed.

We discuss a cosmological Friedmann model modified by inclusion of off-shell matter which has an equation of state $p,\rho \propto T^5,$ $p=1/4\rho .$ Such matter is shown to have energy density comparable with that of non-interacting radiation at temperatures of the order of the Hagedorn temperature, $\sim 10^{12}$ K, indicating the possibility of a phase transition. It is argued that the $T^5$-phase, or an admixture, lies below the high-temperature $T^4$-phase.

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 included

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.

We discuss the properties of an ideal relativistic gas of events possessing Bose-Einstein statistics. We find that the mass spectrum of such a system is bounded by $\mu \leq m\leq 2M/\mu _K,$ where $\mu $ is the usual chemical potential, $M$ is an intrinsic dimensional scale parameter for the motion of an event in space-time, and $\mu _K$ is an additional mass potential of the ensemble. For the system including both particles and antiparticles, with nonzero chemical potential $\mu ,$ the mass spectrum is shown to be bounded by $|\mu |\leq m\leq 2M/\mu _K,$ and a special type of high-temperature Bose-Einstein condensation can occur. We study this Bose-Einstein condensation, and show that it corresponds to a phase transition from the sector of continuous relativistic mass distributions to a sector in which the boson mass distribution becomes sharp at a definite mass $M/\mu _K.$ This phenomenon provides a mechanism for the mass distribution of the particles to be sharp at some definite value.

The relativistic distribution for indistinguishable events is considered in the mass-shell limit $m^2\cong M^2,$ where $M$ is a given intrinsic property of the events. The characteristic thermodynamic quantities are calculated and subject to the zero-mass and the high-temperature limits. The results are shown to be in agreement with the corresponding expressions of an on-mass-shell relativistic kinetic theory. The Galilean limit $c\rightarrow \infty ,$ which coincides in form with the low-temperature limit, is considered. The theory is shown to pass over to a nonrelativistic statistical mechanics of indistinguishable particles., Comment: Report TAUP-2136-94

We find the equation of state $p,\rho \propto T^6,$ which gives the value of the sound velocity $c^2=0.20,$ in agreement with the ``realistic'' equation of state for hot hadronic matter suggested by Shuryak, in the framework of a covariant relativistic statistical mechanics of an event--anti-event system with small chemical and mass potentials. The relativistic mass distribution for such a system is obtained and shown to be a good candidate for fitting hadronic resonances, in agreement with the phenomenological models of Hagedorn, Shuryak, {\it et al.} This distribution provides a correction to the value of specific heat 3/2, of the order of 5.5\%, at low temperatures., Comment: 19 pages, report TAUP-2161-94

The low-temperature form of the equilibrium relativistic mass distribution is subject to the Galilean limit by taking $c\rightarrow \infty .$ In this limit the relativistic Maxwell-Boltzmann distribution passes to the usual nonrelativistic form and the Dulong-Petit law is recovered., Comment: TAUP-2081-93

The relativistic Maxwell-Boltzmann distribution for the system of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered without the simplifying approximation $m^2\cong M^2$, where $M$ is a given intrinsic property of the events. The relativistic mass distribution is obtained and the average values of $m$ and $m^2$ are calculated. The average value of the energy in nonrelativistic limit gives a correction of the order of 10\% to the Dulong-Petit law. Expressions for the pressure and the density of events are obtained and the ideal gas law is recovered., Comment: TAUP-2048-93