D-Brane Recoil and Logarithmic Operators
  We construct the pair of logarithmic operators associated with the recoil of a $D$-brane. This construction establishes a connection between a translation in time and a world-sheet rescaling. The problem of measuring the centre of mass coordinate of the $D$-brane is considered and the relation between the string uncertainty principle and the logarithmic operators is discussed. 
Ian I. Kogan, Nick E. Mavromatos and John F. Wheater