3 research outputs found
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 where is the usual chemical
potential, is an intrinsic dimensional scale parameter for the motion of an
event in space-time, and is an additional mass potential of the
ensemble. For the system including both particles and antiparticles, with
nonzero chemical potential the mass spectrum is shown to be bounded by
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 This phenomenon
provides a mechanism for the mass distribution of the particles to be sharp at
some definite value.Comment: Latex, 22 page
Eikonal Approximation to 5D Wave Equations as Geodesic Motion in a Curved 4D Spacetime
We first derive the relation between the eikonal approximation to the Maxwell
wave equations in an inhomogeneous anisotropic medium and geodesic motion in a
three dimensional Riemannian manifold using a method which identifies the
symplectic structure of the corresponding mechanics. We then apply an analogous
method to the five dimensional generalization of Maxwell theory required by the
gauge invariance of Stueckelberg's covariant classical and quantum dynamics to
demonstrate, in the eikonal approximation, the existence of geodesic motion for
the flow of mass in a four dimensional pseudo-Riemannian manifold. These
results provide a foundation for the geometrical optics of the five dimensional
radiation theory and establish a model in which there is mass flow along
geodesics. Finally we discuss the case of relativistic quantum theory in an
anisotropic medium as well. In this case the eikonal approximation to the
relativistic quantum mechanical current coincides with the geodesic flow
governed by the pseudo-Riemannian metric obtained from the eikonal
approximation to solutions of the Stueckelberg-Schr\"odinger equation. This
construction provides a model for an underlying quantum mechanical structure
for classical dynamical motion along geodesics on a pseudo-Riemannian manifold.
The locally symplectic structure which emerges is that of Stueckelberg's
covariant mechanics on this manifold.Comment: TeX file. 17 pages. Rewritten for clarit