  We study the space of Killing fields on the four dimensional AdS spacetime
$AdS^{3,1}$. Two subsets $\mathcal{S}$ and $\mathcal{O}$ are identified:
$\mathcal{S}$ (the spinor Killing fields) is constructed from imaginary Killing
spinors, and $\mathcal{O}$ (the observer Killing fields) consists of all
hypersurface orthogonal, future timelike unit Killing fields. When the
cosmology constant vanishes, or in the Minkowski spacetime case, these two
subsets have the same convex hull in the space of Killing fields. In presence
of the cosmology constant, the convex hull of $ \mathcal{O}$ is properly
contained in that of $\mathcal{S}$. This leads to two different notions of
energy for an asymptotically AdS spacetime, the spinor energy and the observer
energy. In [10], Chru\'sciel, Maerten and Tod proved the positivity of the
spinor energy and derived important consequences among the related conserved
quantities. We show that the positivity of the observer energy follows from the
positivity of the spinor energy. A new notion called the "rest mass" of an
asymptotically AdS spacetime is then defined by minimizing the observer energy,
and is shown to be evaluated in terms of the adjoint representation of the Lie
algebra of Killing fields. It is proved that the rest mass has the desirable
rigidity property that characterizes the AdS spacetime.
