PHASE OPERATOR AND LATTICE GREENS-FUNCTION FOR RING-LATTICE MODEL IN P-TH NEAREST-NEIGHBOR INTERACTION APPROXIMATION

In dealing with the one-dimensional lattice model, we replace the trad itionally needed Born-Von-Karmann periodic boundary condition with two additional Hamiltonian terms to make up a ring-lattice. In so doing, a unitary phase operator and the corresponding Hermite phase angle ope rator can be introduced as those in quantum optics theory. The new Ham iltonian is invariant under the phase shift transformation. Moreover, the lattice Green's function in the p-th nearest interaction approxima tion can also be easily derived from the new Hamiltonian which becomes the well-known lattice Green's function when the ring is infinite.