STATISTICAL-MECHANICS OF THE MAGNETIZED PAIR QUANTUM GASES

In this report, we present a full study of the statistical mechanics of the zero-field and magnetized pair-boson and pair-fermion gases in d spatial dimensions. An extensive literature has developed over the past decade on the zero-field pair gases. These studies are extensively reviewed and further developed, and we give explicitly results for various thermodynamic functions, such as the specific heat. For the Bose gas, this allows us to give a thorough exposition of d-dimensional pair Bose-Einstein condensation. The generalization to an original study of the statistical mechanics of the magnetized pair quantum gases forms the remaining body of this report. The results presented give a complete investigation, again in d-dimensions, of these systems which are considerably more intricate than their zero-field counterparts. For the Bose gas, we show that although Bose-Einstein condensation does occur tor all d greater-than-or-equal-to 5, the magnetization for all d greater-than-or-equal-to 3 is remarkably different in form to that of the nonrelativistic Bose gas. There is still a Meissner effect, but of a new nature; in fact magnetized pair Bose systems are relativistic superconductors. In the case of the zero-field pair Fermi gas, we review the existing literature, and develop expansions for various thermodynamic functions. For the pair-fermion-gas in an external magnetic field, we find new results for relativistic para/diamagnetism. In this case, the effect of intrinsic spin upon the magnetization is an important one. For both systems, external fields ranging in strength from weak to extremely strong are considered. The physical scenarios for the manifestation of these systems are thus many, and include exotic stellar objects in the present epoch, and cosmology and the early universe. Using these contexts as a background, the emphasis of this report is on the statistical mechanics of pair systems. The Mellin-transform technique is used to develop expansions for the thermodynamic functions, and we give a full presentation of this and other analytical machinery that is necessary to deal with the inherent mathematical intricacy of calculating the relevant thermodynamic functions. This complete study of the zero-field and magnetized Bose and Fermi gases allows comparison between th effects of critical phenomena, thermal pair creation, statistics, spin, and external fields upon the macroscopic behaviour of these fundamental pair systems at temperatures above pair threshold.