  We verify the global Poincar\'e invariance of the Hamiltonian mechanics of
gravitating binary dynamics at the second post Minkowskian (2PM) order. For
spinless point particles, based on the known 2PM Hamiltonian in the center of
momentum frame, we compute the general 2PM Hamiltonian valid in an arbitrary
reference frame. An off-shell extension of the 1PM Hamiltonian, which
contributes at the 2PM order through an iteration process, plays a crucial
role. We then construct the 2PM boost generator that uniquely satisfies all the
conditions imposed by the Poincar\'e algebra.

High Energy Physics - Theory