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A New Relativistic High Temperature Bose-Einstein Condensation

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 $μ\leq m\leq 2M/μ_K,$ where $μ$ is the usual chemical potential, $M$ is an intrinsic dimensional scale parameter for the motion of an event in space-time, and $μ_K$ is an additional mass potential of the ensemble. For the system including both particles and antiparticles, with nonzero chemical potential $μ,$ the mass spectrum is shown to be bounded by $|μ|\leq m\leq 2M/μ_K,$ 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 $M/μ_K.$ This phenomenon provides a mechanism for the mass distribution of the particles to be sharp at some definite value.