The problem of the Fermi-edge singularity in a one-dimensional Tomonaga-Luttinger liquid is reconsidered. The backward scattering of the conduction band electrons on the impuritylike hole in the valence band is analyzed by mapping the problem onto a Coulomb gas theory. For the case when the electron-electron interaction is repulsive, the obtained exponent of the one-dimensional Fermi-edge singularity appears to be different from the exponent found in previous studies. It is shown that the infrared physics of the Fermi-edge singularity in the presence of backward scattering and electron-electron repulsion resembles the physics of the Kondo problem. © 1996 The American Physical Society.

• Received 18 September 1995

DOI:https://doi.org/10.1103/PhysRevB.53.10928