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We consider the energy-momentum excitation spectrum of diverse lattice Hamiltonian operators: the generator of the Markov semi-group of Ginzburg-Landau models with Langevin stochastic dynamics, the Hamiltonian of a scalar quantum field theory and the Hamiltonian associated with the transfer matrix of a classical ferromagnetic spin system at high temperature. The low-lying spectrum consists of a one-particle state and a two-particle band. The two-particle spectrum is determined using a lattice version of the Bethe-Salpeter equation. In addition to the two-particle band, depending on the lattice dimension and on the attractive or repulsive character of the interaction between the particles of the system, there is, respectively, a bound state below or above the two-particle band. We show how the existence or non-existence of these bound states can be understood in terms of non-relativistic single and two-particle lattice Schrödinger Hamiltonians with a delta potential; the corresponding resolvent equations are related to the Bethe-Salpeter equation. It turns out that a staggering transformation relates the spectrum of the attractive case to the corresponding spectrum for the repulsive case for each model we analyze. PACS number(s): 02.50.-r, 02.30.Tb, 05.50.+q, 11.10.St, 75.10.Hk, 02.50.Ga

Staggering tranformations and the excitation spectrum of diverse lattice quantum models