  It is shown that a general radial conformal Killing vector in Minkowski
space-time can be associated to a generator of time evolution in conformal
quantum mechanics. Among these conformal Killing vectors one finds a class
which maps causal diamonds in Minkowski space-time into themselves. The flow of
such Killing vectors describes worldlines of accelerated observers with a
finite lifetime within the causal diamond. Time evolution of static diamond
observers is equivalent to time evolution in conformal quantum mechanics
governed by a hyperbolic Hamiltonian and covering only a segment of the time
axis. This indicates that the Unruh temperature perceived by static diamond
observers in the vacuum state of inertial observers in Minkowski space can be
obtained from the behaviour of the two-point functions of conformal quantum
mechanics.
