  We study the ground state properties of spin-half bosons subjected to the
Rashba spin-orbit coupling in two dimensions. Due to the enhancement of the low
energy density of states, it is expected that the effect of interaction becomes
more important. After reviewing several possible ideal condensed states, we
carry out an exact diagonalization calculation for a cluster of the bosons in
the presence of strong spin-orbit coupling on a two-dimensional disk and reveal
strong correlations in its ground state. We derive a low-energy effective
Hamiltonian to understand how states with strong correlations become
energetically more favorable than the ideal condensed states.
