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'nikov 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 Schrodinger operators; Problems and results.
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'nikov 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 Schrodinger operators; Problems and results.