NON-REDUCIBLE REPRESENTATIONS OF GENERAL COMMUTATION CORRELATIONS. CONSERVATION LAWS AND ASYMPTOTICS OF SPECTRUM IN QUANTUM HAMILTONIANS

Abstract

For commutation correlations in which the production operator, annihilation operator and, possible, operator of the particle number figure, all the possible types of the non-reducible representations in which the product of the production and annihilation operators has even if one non-zero own vector have been found. The classified theorems have been proved. For one wide class of the quantum Hamiltonians, the problem of finding all the conservation laws represented as a function from operators of the particle number is considered. The conditions quaranting the presence of such conservation laws and also the application-comfortable criterion of presenting the conservation laws being linear according to the particle number operators have been obtained. Application field: construction of new mathematical models and solution of applied problems in the field of quantum optics, quantum theory of field and kinetic theory of gases; investigation of quantum Hamiltonian spectrumAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio