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Singular Quadratic Forms in Perturbation Theory de Volodymyr Koshmanenko

Singular Quadratic Forms in Perturbation Theory: Mathematics and Its Applications, cartea 474

Autor Volodymyr Koshmanenko
en Limba Engleză Paperback – 10 oct 2012
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(
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Specificații

ISBN-13: 9789401059527
ISBN-10: 9401059527
Pagini: 324
Ilustrații: VIII, 312 p.
Dimensiuni: 160 x 240 x 17 mm
Greutate: 0.45 kg
Ediția:Softcover reprint of the original 1st ed. 1999
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and Its Applications

Locul publicării:Dordrecht, Netherlands

Public țintă

Research

Cuprins

1. Quadratic Forms and Linear Operators.- 1. Preliminary Facts about Quadratic Forms.- 2. Closed and Closable Quadratic Forms.- 3. Operator Representations of Quadratic Forms.- 4. Quadratic Forms in the Theory of Self-Adjoint Extensions of Symmetric Operators.- 2. Singular Quadratic Forms.- 5. Definition of Singular Quadratic Forms.- 6. Properties of Singular Quadratic Forms.- 7. Operator Representation of Singular Quadratic Forms.- 8. Singular Quadratic Forms in the A-Scale of Hilbert Spaces.- 9. Regularization.- 3. Singular Perturbations of Self-Adjoint Operators.- 10. Rank-One Singular Perturbations.- 11. Singular Perturbations of Finite Rank.- 12. Method of Self-Adjoint Extensions.- 13. Powers of Singularly Perturbed Operators.- 14. Method of Orthogonal Extensions.- 15. Approximations.- 4. Applications to Quantum Field Theory.- 16. Singular Properties of Wick Monomials.- 17. Orthogonally Extended Fock Space.- 18. Scattering and Spectral Problems.- References.- Notation.

Recenzii

` ...this text is a valuable contribution to the literature on the abstract aspects of singular perturbation theory.'
Mathematical Reviews, 2001a