  Magnetic monopoles are suggested to play an important role in strongly
coupled quark-gluon plasma (sQGP) near the deconfinement temperature. So far,
their many-body treatment has only been done classically, with just binary
scattering solved in quantum mechanics. In this paper we start quantum
many-body studies of the monopole ensembles. Specifically, we carry out
numerical simulations of the path integral for one- and two-component Coulomb
Bose systems. We determine the relation between the critical temperature for
the Bose-Einstein condensation phase transition $T_\text{c}$ and the Coulomb
coupling strength using two methods, the classic finite-size scaling of the
condensate and a lattice-tested method based on permutation cycles. For a
one-component Coulomb Bose gas, we observe the same behavior of the critical
temperature -- initially rising slightly then falling as interaction strength
is increased -- as seen in the case of hard spheres; we also observe the same
behavior for a two-component Coulomb Bose gas. We then calculate sets of radial
correlation functions between the like and unlike charged particles. By
matching those with the correlation functions previously calculated on the
lattice, we derive an effective quantum model of color magnetic monopoles in
QCD. From this matched model, we are able to extract the monopole contribution
to QCD equation of state near $T_\text{c}$.
