This monograph is devoted to the systematic presentation of the method of singular quadratic forms in the perturbation theory of self-adjoint operators.
The concept of a singular (nowhere closable) quadratic form, a key notion of the present volume, is treated from different points of view such as definition, properties, relations with regular (closable) quadratic forms, operator representation, classification in the scale of Hilbert spaces and especially as an object carrying a singular perturbation for Hamiltonians. The main idea is to interpret singular quadratic form in the role of an abstract boundary condition for self-adjoint extension. Various aspects of the singularity principle are investigated, such as the construction of singularly perturbed operators, higher powers of perturbed operators, the transition to a new orthogonally extended state space, as well as approximation and regularization. Furthermore, applications dealing with singular Wick monomials in the Fock space and mathematical scattering theory are included.
Audience: This book will be of interest to students and researchers whose work involves functional analysis, operator theory and quantum field theory.
` ...this text is a valuable contribution to the literature on the abstract aspects of singular perturbation theory.' Mathematical Reviews, 2001a
|Preface to the English Edition|
|Quadratic Forms and Linear Operators|
|Singular Quadratic Forms|
|Singular Perturbations of Self-Adjoint Operators|
|Applications to Quantum Field Theory|
|Table of Contents provided by Publisher. All Rights Reserved.|
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Number Of Pages: 312
Published: 30th April 1999
Country of Publication: NL
Dimensions (cm): 24.77 x 17.78 x 2.54
Weight (kg): 0.59