  The gas of interacting excitons in quantum wells is studied. We obtain the
Hamiltonian of this gas by the projection of the electron-hole plasma
Hamiltonian to exciton states and an expansion in a small density. Matrix
elements of the exciton Hamiltonian are rather sensitive to the geometry of the
heterostructure. The mean field approximation of the exciton Hamiltonian gives
the blue shift and spin splitting of the exciton luminescence lines. We also
write down the Boltzmann equation for excitons and estimate the energy and spin
relaxation time resulting from the exciton-exciton scattering. Making use of
these calculations we succeeded to explain some recent experimental results
which have not been explained so far.
