In this paper the quantum covariant relativistic dynamics of many bodies is reconsidered. It is emphasized that this is an event dynamics. The events are quantum statistically correlated by the global parameter τ. The derivation of an event Boltzmann equation emphasizes this. It is shown that this Boltzmann equation may be viewed as exact in a dilute event limit ignoring three event correlations. A quantum entropy principle is obtained for the marginal Wigner distribution function. By means of event linking (concatenations) particle properties such as the equation of state may be obtained. We further reconsider the generalized quantum equilibrium ensemble theory and the free event case of the Fermi-Dirac and Bose-Einstein distributions, and some consequences. The ultra-relativistic limit differs from the non-covariant theory and is a test of this point of view.
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References
R. Balescu (1964) Cargese Summer School Gordon and Breach New York
R. Balescu T. Kotera (1967) Physica. 33 558
H. A. Bethe E. E. Saltpeter (1957) The Quantum Mechanics of One and Two Electron Atoms Academic Press New York
N. N. Bogoliubov (1946) “Problems Dynamical in Statistical Physics,” translated by E.K. Gora G. E. Uhlenbeck J. Boer Particlede (Eds) Studies in Statistical Mechanics I North Holland Amsterdam
L. Boltzmann (1964) Lectures on Gas Theory, translated by S.G. Brush. University of California Press Berkeley
L. Burakovski L. P. Horwitz (1993) Physica. A 201 666 Occurrence Handle1993PhyA..201..666B
L. Burakovski L. P. Horwitz W. C. Schieve (1996) Phys. Rev. D. 54 4029 Occurrence Handle1996PhRvD..54.4029B
L. Burakovski, L. P. Horwitz, and W. C. Schieve, “Mass-Proper Time Uncertainty Relations in a Manifestly Covariant Relativistic Statistical Mechanics,” preprint (1996).
L. Burakovski L. P. Horwitz (1997) Nuclear Phys. A. 614 373 Occurrence Handle1997NuPhA.614..373B
J.L. Cook (1972) Aust. J. Phys. 25 117 Occurrence Handle1972AuJPh..25..117C
S. R. Groot Particlede C. K. Leeuwen Particlevan G. Weert Particlevan (1980) Relativistic Kinetic Theory North Holland New York
J. Ehlers, in Lectures in Statistical Physics 28, W. C. Schieve and J. S. Turner eds. (Springer, New York, 1974).
A. Einstein (1922) The Meaning of Relativity Princeton University Press Princeton, New Jersey
J.R. Fanchi (1993) Parametrized Relativistic Quantum Theory Kluwer Dordrecht
R.P. Feynman (1949) Phys. Rev. 76 746 Occurrence Handle1949PhRv...76..749F Occurrence Handle11,765d
H. Goldstein (1980) Classical Mechanics EditionNumber2 Addison-Wesley Reading, Massachusetts
R. Hakim (1967) J. Math. Phys. 8 1315–1379
P. Havas, Statistical Mechanics of Equilibrium and Non-Equilibrium, Meixner eds. (North Holland, Amsterdam, 1965).
L. P. Horwitz C. Piron (1973) Helv. Physica. Acta. 46 316
L. P. Horwitz W. C. Schieve C. Piron (1981) Ann of Phys, N.Y. 137 306 Occurrence Handle83e:82004
Horwitz L.P., from Old and New Questions in Physics,ed. by van der Merwe (Plenon, New York, 1983).
L.P. Horwitz Y. Lavie (1983) Phys Rev D. 26 819 Occurrence Handle1982PhRvD..26..819H Occurrence Handle83h:81082
L.P. Horwitz S. Shashoua W.C. Schieve (1989) Physica A. 161 300 Occurrence Handle10.1016/0378-4371(89)90471-8 Occurrence Handle1989PhyA..161..300H Occurrence Handle90j:82022
R. Hudson (1974) Rep. Math. Phys. 6 249 Occurrence Handle0324.60018 Occurrence Handle52 #4896
F. Juttner (1911) Ann. Phys., Leipzig. 34 856
H. Kandrup (1984) Ann. Phys. N.Y. 153 44 Occurrence Handle10.1016/0003-4916(84)90184-2 Occurrence Handle85k:82004b
R. L. Liboff (1998) Kinetic Theory EditionNumber3 Springer Verlag New York
J. A. McLennan (1989) Introduction to Non-Equilibrium Statistical Mechanics Prentice Hall New York
W. Pauli (1958) Theory of Relativity Pergamon New York
F. Rohrlich (1961) Ann. Phys. N.Y. 13 93 Occurrence Handle10.1016/0003-4916(61)90028-8 Occurrence Handle0098.19903 Occurrence Handle26 #5847
E. V. Shuryak (1988) The QCD Vacuum, Hadrons and Superdense Matter World Scientific Singapore
E.C.G. Stueckelberg (1941) Helv. Phys. Acta. 14 588 Occurrence Handle0026.17703 Occurrence Handle4,56f
J.L. Synge (1957) Relativistic Gas Thyeory North Holland Amsterdam
J. R. Taylor (1972) Scattering Theory John Wiley New York
R.C. Tolman (1967) Principles of Statistical Mechanics Oxford University Press London
M.A. Trump W.C. Schieve (1999) Classical Relativistic Many-Body Dynamics Kluwer Dordrecht
E.P. Wigner (1932) Phys. Rev. 49 2127
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Schieve, W.C. Covariant Relativistic Statistical Mechanics of Many Particles. Found Phys 35, 1359–1381 (2005). https://doi.org/10.1007/s10701-005-6441-9
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DOI: https://doi.org/10.1007/s10701-005-6441-9