Central charges and Hamiltonians for 0-brane dynamics - art. no. 084007.

We consider the general properties of central charges of 0-branes and assoc iated duality invariants, in view of their double role, on the bulk and on the world volume (quantum mechanical) theory. A detailed study of the BPS c ondition for the mass spectrum arising from toroidal compactifications is g iven for 1/2, 1/4, and 1/8 BPS states in any dimension. As a by-product, we retrieve the U-duality invariant conditions on the charge (zero mode) spec trum and the orbit classification of BPS states preserving different fracti ons of supersymmetry. The BPS condition for 0-branes in theories with 16 su persymmetries in any dimension is also discussed. [S0556-2821(99)01716-6].