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.

Table of Contents

• Zh. I. Abdullaev and S. N. Lakaev -- On the spectral properties of the matrix-valued Friedrichs model
• D. D. Botvich and V. A. Malyshev -- Asymptotic completeness and all that for an infinite number of fermions
• A. M. Mel'ikov and R. A. Minlos -- On the pointlike interaction of three different particles
• R. A. Minlos and E. A. Zhizhina -- Meson states in lattice QCD
• A. I. Mogilner -- Hamiltonians in solid-state physics as multiparticle discrete Schrödinger operators: Problems and results