Renormalized frequency shift of a Wannier exciton in a one-dimensional system

The radiative frequency shift of superradiant exciton in a one-dimensional system is calculated. It is shown that a finite frequency shift can be obtained after proper renormalization. The value of the shift is inversely proportional to the factor $\frac{\lambda }{d}$, where $\lambda$ is the wavelength of the emitted photon and $d$ is the lattice spacing.