Remarks on the use of group theory in quantum optics

The relationships between certain important nonclassical states of the quan tized field and the coherent states associated with the SU(2) and SU(1,1) L ie groups and associated Lie algebras is briefly reviewed. As an example of the utility of group theoretical methods in quantum optics, a method for g enerating maximally entangled photonic states is discussed. These states ma y be of great importance for achieving Heisenberg-limited interferometry an d in beating the diffraction limit in lithography. (C) 2001 Optical Society of America.