Spectrum and eigenfunctions of the transfer matrix of a two-dimensional Gaussian model

For a Gaussian model on a two-dimensional lattice a family of commuting transfer matrices is constructed. The spectrum and eigenfunctions of a transfer matrix are found. The unitarity relation for the transfer matrix is satisfied on a finite lattice up to a numerical factor which tends to unity in the limit of an infinite lattice. The transfer matrix leads to a local Hamiltonian of a free massive scalar field.