  We apply a recent proposal for a distinguished ground state of a quantum
field in a globally hyperbolic spacetime to the free massless scalar field in a
causal diamond in two-dimensional Minkowski space. We investigate the two
limits in which the Wightman function is evaluated (i) for pairs of points that
lie in the centre of the diamond (i.e. far from the boundaries), and (ii) for
pairs of points that are close to the left or right corner. We find that in the
centre, the Minkowski vacuum state is recovered, with a definite value of the
infrared cutoff. Interestingly, the ground state is not the Rindler vacuum in
the corner of the diamond, as might have been expected, but is instead the
vacuum of a flat space in the presence of a static mirror on that corner. We
confirm these results by numerically evaluating the Wightman function of a
massless scalar field on a causal set corresponding to the continuum causal
diamond.
