The absorption of electromagnetic waves in molecular crystals at low temperature has been studied using the Green's-function method. The spin dependence of the excitations created by photon absorption has been explicitly considered. In the Hartree-Fock (HF) approximation and in the absence of the radiation field, the poles of the exciton Green's function consist of two frequency modes corresponding to the singlet and triplet exciton fields, respectively, and propagate through the medium independently; beyond the HF approximation, the two modes are no longer independent. The spectral function for the photon field is found to consist of the superposition of symmetric and asymmetric Lorentzian lines. General expressions for the energy shift and spectral width are derived. An example is worked out for the resonance Raman scattering of triplet excitions, where the incident photon becomes a polariton and then decays into two triplet excitons. Physical processes, where a singlet exciton decays into two triplet excitons, as well as the excitation spectrum of triplet excitons, have been studied in detail.