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 [Formula presented], where [Formula presented] is the usual chemical potential, [Formula presented] is an intrinsic dimensional scale parameter for the motion of an event in space time, and [Formula presented] is an additional mass potential of the ensemble. For the system including both particles and antiparticles, with a nonzero chemical potential [Formula presented], the mass spectrum is shown to be bounded by [Formula presented], 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 [Formula presented]. This phenomenon provides a mechanism for the mass distribution of the particles to be sharp at some definite value.