New relativistic high-temperature Bose-Einstein condensation.

Abstract

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 $\ensuremath{\mu}<~m<~2\frac{M}{{\ensuremath{\mu}}_{K}}$, where $\ensuremath{\mu}$ is the usual chemical potential, $M$ is an intrinsic dimensional scale parameter for the motion of an event in space time, and ${\ensuremath{\mu}}_{K}$ is an additional mass potential of the ensemble. For the system including both particles and antiparticles, with a nonzero chemical potential $\ensuremath{\mu}$, the mass spectrum is shown to be bounded by $|\ensuremath{\mu}|<~m<~2\frac{M}{{\ensuremath{\mu}}_{K}}$, 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 $\frac{M}{{\ensuremath{\mu}}_{K}}$. This phenomenon provides a mechanism for the mass distribution of the particles to be sharp at some definite value.