Direct Interactions in Relativistic Statistical Mechanics

Directly interacting particles are considered in the multitime formalism of predictive relativistic mechanics. When the equations of motion leave a phase-space volume invariant, it turns out that the phase average of any first integral, covariantly defined as a flux across a $7n$-dimensional surface, is conserved. The Hamiltonian case is discussed, a class of simple models is exhibited, and a tentative definition of equilibrium is proposed.Comment: Plain Tex file, 26 page

Gauging kinematical and internal symmetry groups for extended systems: the Galilean one-time and two-times harmonic oscillators

The possible external couplings of an extended non-relativistic classical system are characterized by gauging its maximal dynamical symmetry group at the center-of-mass. The Galilean one-time and two-times harmonic oscillators are exploited as models. The following remarkable results are then obtained: 1) a peculiar form of interaction of the system as a whole with the external gauge fields; 2) a modification of the dynamical part of the symmetry transformations, which is needed to take into account the alteration of the dynamics itself, induced by the {\it gauge} fields. In particular, the Yang-Mills fields associated to the internal rotations have the effect of modifying the time derivative of the internal variables in a scheme of minimal coupling (introduction of an internal covariant derivative); 3) given their dynamical effect, the Yang-Mills fields associated to the internal rotations apparently define a sort of Galilean spin connection, while the Yang-Mills fields associated to the quadrupole momentum and to the internal energy have the effect of introducing a sort of dynamically induced internal metric in the relative space.Comment: 32 pages, LaTex using the IOP preprint macro package (ioplppt.sty available at: http://www.iop.org/). The file is available at: http://www.fis.unipr.it/papers/1995.html The file is a uuencoded tar gzip file with the IOP preprint style include

Relativistic Corrections in a Three-Boson System of Equal Masses

Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the mass-shell constraints can be reduced to a three-dimensional eigenvalue problem. In general, this problem is complicated, but for three equal masses a drastic simplification arises at the first post-Galilean order: the reduced wave equation becomes tractable, and we can compute a first-order correction beyond the nonrelativistic limit. The harmonic interaction is displayed as a toy model.Comment: 16 pages, no figure. Several points clarified, one typo corrected. References added. To appear in Physical Review

Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments

A large number of treatments of the meson spectrum have been tried that consider mesons as quark - anti quark bound states. Recently, we used relativistic quantum "constraint" mechanics to introduce a fully covariant treatment defined by two coupled Dirac equations. For field-theoretic interactions, this procedure functions as a "quantum mechanical transform of Bethe-Salpeter equation". Here, we test its spectral fits against those provided by an assortment of models: Wisconsin model, Iowa State model, Brayshaw model, and the popular semi-relativistic treatment of Godfrey and Isgur. We find that the fit provided by the two-body Dirac model for the entire meson spectrum competes with the best fits to partial spectra provided by the others and does so with the smallest number of interaction functions without additional cutoff parameters necessary to make other approaches numerically tractable. We discuss the distinguishing features of our model that may account for the relative overall success of its fits. Note especially that in our approach for QCD, the resulting pion mass and associated Goldstone behavior depend sensitively on the preservation of relativistic couplings that are crucial for its success when solved nonperturbatively for the analogous two-body bound-states of QED.Comment: 75 pages, 6 figures, revised content

Classical relativistic statistical mechanics: The case of a hot dilute plasma

Starting from predictive relativistic mechanics we develop a classical relativistic statistical mechanics. For a system of N particles, the basic distribution function depends, in addition to the 6N coordinates and velocities, on N times, instead of a single one as in the usual statistical mechanics. This generalized distribution function obeys N (instead of 1) continuity equations, which give rise to N Liouville equations in the case of a dilute plasma (i.e., to lowest, nonzero order in the charges). Hence, the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for the reduced generalized distribution functions is derived. A relativistic Vlasov equation is obtained in this way. Thermal equilibrium is then considered for a dilute plasma. The calculation is explicitly worked out for a weakly relativistic plasma, up to order 1/c2, and known results are recovered