title: Excitation spectrum and staggering transformations in lattice quantum models.
abstract: We consider the energy-momentum excitation spectrum of diverse lattice Hamiltonian operators: the generator of the Markov semigroup 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 nonexistence of these bound states can be understood in terms of a nonrelativistic single-particle lattice Schrödinger Hamiltonian with a delta potential. A staggering transformation relates the spectra of the attractive and the repulsive cases.
authors.affiliation: Departamento de Matemática, ICMC-USP, Caixa Postal 668, 13560-970 São Carlos, São Paulo, Brazil. veiga@icmc.sc.usp.br
authors.forename: Paulo A
authors.initials: PA
authors.lastname: Faria da Veiga
authors.forename: Michael
authors.initials: M
authors.lastname: O'Carroll
authors.forename: Ricardo
authors.initials: R
authors.lastname: Schor