Inverse operator representations of quantum phase
  We define quantum phase in terms of inverses of annihilation and creation operators. We show that like Susskind - Glogower phase operators, the measured phase operators and the unitary phase operators can be defined in terms of the inverse operators. However, for the unitary phase operator the Hilbert space includes the negative energy states. The quantum phase in inverse operator representation may find the applications in the field of quantum optics particularly in the squeezed states. 
G.M. Saxena