Singular Quadratic Forms in Perturbation Theory [Hardcover]

The notion of singular quadratic form appears in mathematical physics as a tool for the investigation of formal expressions corresponding to perturbations devoid of operator sense. Numerous physical models are based on the use of Hamiltonians containing perturba? tion terms with singular properties. Typical examples of such expressions are Schrodin? ger operators with O-potentials (-~ + AD) and Hamiltonians in quantum field theory with perturbations given in terms of operators of creation and annihilation (P(The notion of singular quadratic form appears in mathematical physics as a tool for the investigation of formal expressions corresponding to perturbations devoid of operator sense. Numerous physical models are based on the use of Hamiltonians containing perturba? tion terms with singular properties. Typical examples of such expressions are Schrodin? ger operators with O-potentials (-~ + AD) and Hamiltonians in quantum field theory with perturbations given in terms of operators of creation and annihilation (P(Preface to the English Edition. Introduction. 1. Quadratic Forms and Linear Operators. 2. Singular Quadratic Forms. 3. Singular Perturbations of Self-Adjoint Operators. 4. Applications to Quantum Field Theory. References. Subject Index. Notation.` ...this text is a valuable contribution to the literature on the abstract aspects of singular perturbation theory.'
Mathematical Reviews, 2001a