It is shown that the Greens function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.
On the basis of a semi-phenomenological model, it is argued that the high energy anomaly observed in recent photoemission experiments on cuprates is caused by interaction with an overdamped bosonic mode in the mid-infrared region of the spectrum. Ana
lysis of optical conductivity allows to connect this excitation to the incoherent charge response reported for the majority of high Tc materials and some other perovskites. We show that its large damping is an essential feature responsible for the waterfall dispersion and linewidth of the spectral weight.
A new expression for the Greens function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered a
s an example. Comparison to Bethe ansatz clarifies the relation between the two approaches.
