  We represent N-body Coulomb energy in a localized form to achieve massive
parallelism. It is a well-known fact that Green's functions can be written as
path integrals of field theory. Since two-body Coulomb potential is a Green's
function of Poisson equations, it reduces to a path integral of free scalar
field theory with three spatial dimensions. This means that N-body one also
reduces to a path integral. We discretize real space with a cubic lattice and
evaluate the obtained multiple integrals approximately with the Markov-chain
Monte Carlo method.
