"These of are very powerful. Let us recall the situation in flat space. If we have a massive in flat space then we can always boost to a . In AdS it is the same: if we consider the oscillating trajectory of a massive particle then we can "boost" to a frame where the particle is at rest. Thus, the moving particle does not know that is moving and, despite appearances, there is no "center" in AdS. The is part of the (as in the ) and there are several choices of Hamiltonian. Once we choose a Hamiltonian ... then we have chosen a "center" and a notion of the , in which a particle sits at this "center.""