  We consider the normalized axisymmetric solutions of Klein-Fock-Gordon
equation with energy spectrum that lies below usual rest energy $mc^{2}$. It is
shown that the gas of hypothetical particles, described by such solutions,
would possess uncommon thermodynamic and kinetic characteristics, in
particular, an anomalously high temperature of Bose-Einstein condensations as
well as - in the case of charged particles - a conductivity, much exceeding
that of conventional plasma.
