Covariant Relativistic Statistical Mechanics of Many Particles

Abstract

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 ultrarelativistic limit differs from the non-covariant theory and is a test of this point of view.

Thermal Equilibrium and Statistical Thermometers in Special Relativity

“…(2) and, in particular, predicts a different mean energy-temperature relation in the ultrarelativistic limit T ! 1 [16]. Since then, partially conflicting results and proposals from other authors [17][18][19][20][21] have led to an increasing confusion as to which distribution actually represents the correct generalization of the Maxwellian (1).…”

“…The above conventions define the simplest interacting model system that (i) complies with all principles of SR, (ii) does not require the introduction of interaction fields, (iii) can be simulated without further approximation, and (iv) exhibits a universal stationary equilibrium state. Hence, this model system provides an optimal test case for probing the predictions of different relativistic kinetic theories by means of numerical experiments [5][6][7][8]14,16]. Moreover, as we shall see below, it helps to clarify long-standing controversial questions regarding the definition and meaning of temperature and thermal equilibrium in SR.…”

Comparative Analysis of Jüttner’s Calculation of the Energy of a Relativistic Ideal Gas and Implications for Accelerator Physics and Cosmology

“…Referring to the parametrized statistical mechanical framework presented by Schieve [15], Debbasch [14] argued in Section 4.2 that "The real and apparently only reason to develop the approach presented in [15] is a historical one, namely the desire to treat relativistic interactions in the framework of action-at-a-distance theories. These theories are today widely considered unrealistic; indeed, not only does the theoretical framework used in [15] allow the (non-quantum) particles to wander off their mass-shells, but action-at-a-distance theories do not seem to permit a theoretical treatment of the particle creation/annihilation phenomenon, which is naturally an experimental fact.…”

“…These theories are today widely considered unrealistic; indeed, not only does the theoretical framework used in [15] allow the (non-quantum) particles to wander off their mass-shells, but action-at-a-distance theories do not seem to permit a theoretical treatment of the particle creation/annihilation phenomenon, which is naturally an experimental fact. "…”

Manifestly covariant classical correlation dynamics I. General theory

“…The fundamental problem of physics of relativistic classical many-body systems is one century old (for a review of early investigations see, e.g., [1]) and, still, remains one of the most important subjects in studies of relativity [2][3][4][5]. At the microscopic level the basis of deterministic classical dynamics of relativistic many-body systems has been widely explored [6][7][8][9].…”