This collection deals with several different topics related to the construction and spectral analysis of Hamiltonians of various systems arising in mathematical physics. Included are a study of the disposition and character of resonances for certain operators, with applications to solid body physics; a survey of work in the perturbation of Hamiltonians in fermion systems; an examination of the construction of the Hamiltonian for three different pointwise interacting quantum particles; and a study of the lower branches of the Hamiltonian of the lattice model for chromodynamics. The final paper presents an extensive survey of problems related to the spectrum of finite-particle lattice Hamiltonians, which arise in quantum field theory and in models in the theory of solid bodies. The book provides an introduction of sorts to a series of new methods and problems in mathematical physics.
On the spectral properties of the matrix-valued Friedrichs model by Zh. I. Abdullaev and S. N. Lakaev Asymptotic completeness and all that for an infinite number of fermions by D. D. Botvich and V. A. Malyshev On the pointlike interaction of three different particles by A. M. Mel$'$nikov and R. A. Minlos Meson states in lattice QCD by R. A. Minlos and E. A. Zhizhina Hamiltonians in solid-state physics as multiparticle discrete Schrodinger operators: Problems and results by A. I. Mogilner.