Fusion rules for the continuum sectors of the Virasoro algebra with c=1
  The Virasoro algebra with c=1 has a continuum of superselection sectors characterized by the ground state energy h. Only a discrete subset of sectors arises by restriction of representations of the SU(2) current algebra at level k=1. The remaining continuum of sectors is obtained with the help of (localized) homomorphisms into the current algebra. The fusion product of continuum sectors with discrete sectors is computed. A new method of determining the sector of a state is used. 
K.-H. Rehren, H.R. Tuneke