The necessary mathematical equipment is developed for an analysis of the zero modes connected with hamiltonians quadratic in boson creation and annihilation operators. A “cross-matrix” being a matrix of a certain partitioned form, we consider the group G of conjuctivity transformations T,...

In the previous paper we have shown that the classification problem of the homogeneous real 16-vertex models on a square lattice as proposed by Gaaff and Hijmans is closely connected with the similar problem corresponding to the boson Bogoliubov transformation in quantum mechanics. This insight...

As a coping-stone of our investigations concerning the general quadratic hamiltonian in a finite set of (boson or fermion) creation and annihilation operators we consider the homogeneous quadratic boson hamiltonian with zero modes. It is proved that zero (soft) modes, as they are connected with...

A general treatment has been given of the problem of diagonalizing a hamiltonian which is a homogeneous quadratic expression in a finite number of boson construction operators. The treatment provides us with several systematic procedures to diagonalize such hamiltonians in practice; each algorithm...