Spectral Theory Of Families Of Self-adjoint Operators

This volume deals with structure theorems and models for finite and countable families of self-adjoint operators which satisfy commutative, noncommutative, Lie and more general relations. Such families are studied because of their relation to mathematical models of quantum systems in theoretical physics, representation theory of Lie groups and Lie algebras, (in particular, large' Lie algebras), and representation of infinitesimal objects of these supergroups and superalgebras. The methods employed are those of commutative and noncommutative probability theory. For mathematicians and physicists whose work involves spectral theory, Lie algebras and probability theory. The book will also be of use to those interested in mathematical models of quantum systems.