Abstract
It is well known that the analysis of a relativistic n-body problem invariant under the transformations of the Poincaré group and involving only one time has only been done for n = 1. For n > 1 one uses the second quantization formalism of field theory. In this paper we state it in the ordinary space time coordinates associated with the n-bodies as Dirac did in the one body case. We apply the formalism first to the two-body problem and have a development of the Hamiltonian in terms of powers of (1/c2), that allows us to determine the spectra of bottomonium and compare with the experimental results.