THE FERMI-EDGE SINGULARITY AND BOUNDARY-CONDITION CHANGING OPERATORS

The boundary conformal field theory approach to quantum impurity problems is used to study the Fermi edge singularity, occurring in the x-ray adsorption probability. The deep-hole creation operator, in the effective low-energy theory, changes the boundary condition on the conduction electrons. By a conformal mapping, the dimension of such an operator is related to the ground-state energy for a finite system with different boundary conditions at the two ends. The Fermi edge singularity is solved, using this method, for the Luttinger liquid including backscattering and for the multi-channel Kondo problem.