  The global Minkowski Bessel (M-B) modes, whose explicit form allows the
identification and description of the condensed vacuum state resulting from the
operation of a pair of accelerated refrigerators, are introduced. They span the
representation space of the unitary representation of the Poincare group on 2-D
Lorentz space-time. Their three essential properties are: (1) they are
unitarily related to the familiar Minkowski plane waves; (2) they form a
unitary representation of the translation group on two dimensional Minkowski
spacetime. (3) they are eigenfunctions of Lorentz boosts around a given
reference event. In addition the global Minkowski Mellin modes are introduced.
They are the singular limit of the M-B modes. This limit corresponds to the
zero transverse momentum solutions to the zero rest mass wave equation.
  Also introduced are the four Rindler coordinate representatives of each
global mode. Their normalization and density of states are exhibited in a
(semi-infinite) accelerated frame with a finite bottom. In addition we exhibit
the asymptotic limit as this bottom approaches the event horizon and thereby
show how a mode sum approaches a mode integral as the frame becomes bottomless.
