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The fine structure of excitons, caused by the electron-hole exchange interaction, is modified in quantum wells due to the reduced symmetry and increased Coulomb interaction. We present a systematic formulation of the exchange interaction for quantum-well excitons and perform numerical calculations of the fine-structure splitting and dispersion for Alp. sGap. &As/GaAs quantum wells. The coupling of quantum-well excitons with the electromagnetic field is formulated in second quantization.By solving the coupled equations of motion for excitons and photons we calculate the dispersion relations for localized and resonant polaritons as well as the radiative lifetime for the resonant modes. Our results agree with those obtained by Andreani and Bassani [Phys. Rev. B 41, 7536 (1990)] and Tassone, Bassani, and Andreani [Nuovo Cimento D 12, 1673(1990], who used Maxwell's equations instead of the quantum field formulation. We draw some conclusions on the fine-structure splitting expected for excitons in quantum wells of II-VI semiconductors.

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