  Gravitational wave observatories targeted for compact binary coalescence,
such as LIGO and VIRGO, require various theoretical inputs for their efficient
detection. One of such inputs are analytical description of binary dynamics at
sufficiently separated orbital scales, commonly known as post-Newtonian
dynamics. One approach for determining such two-body effective Hamiltonians is
to use quantum scattering amplitudes.
  This dissertation aims at an improved understanding of classical physics of
spinning bodies in quantum scattering amplitudes, for application to the
problem of effective two-body Hamiltonians. The main focus will be on
spin-induced higher-order multipole moments. In this dissertation results for
the first post-Minkowskian order (linear in Newton's constant $G$ and to all
orders in relative momentum $p^2$) Hamiltonian that is valid for arbitrary
compact spinning bodies to all orders in spin is presented. Next, obstruction
and prospects for the formulation's extension to second post-Minkowskian order
is discussed, based on an equivalent loop order quantum field theory
computations.
  This dissertation is based on the works [1-4].
