Many‐Body Theory for the Dense Exciton Gas of Direct Semiconductors I. General Considerations

The dense exciton gas is studied theoretically using the two‐time electron–hole pair propagator. The equation of motion for the propagator and an expression for the electron–hole pair selfenergy are transformed to a picture in which electron–hole pairs are mapped on bosons. The lowest decoupling of the selfenergy provides contributions of first and second order concerning the interaction between electron–hole pairs including electron–electron, hole–hole, and electron–hole pair exchange. It is shown that only the direct interaction between electron–hole pairs can be screened by a dielectric function. The connection with results obtained on the basis of an effective Hamiltonian for bosonic electron–hole pairs is discussed.