We consider the problem of bosonic particles interacting repulsively i
n a strong magnetic field at the filling factor v = 1. We project the
system in the lowest Landau level and set up a formalism to map the dy
namics into an interacting fermion system. Within a mean field approxi
mation we find that the composite fermions behave as a gas oi neutral
dipoles and we expect that the low energy limit also describes the phy
sical v = 1/2 fermionic state. (C) 1998 Elsevier Science B.V.