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Singular Quadratic Forms in Perturbation Theory




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Dettagli

Genere:Libro
Lingua: Inglese
Pubblicazione: 04/1999
Edizione: 1999





Trama

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(




Sommario

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.










Altre Informazioni

ISBN:

9780792356257

Condizione: Nuovo
Collana: Mathematics and Its Applications
Dimensioni: 244 x 170 mm
Formato: Copertina rigida
Illustration Notes:VIII, 312 p.
Pagine Arabe: 312
Pagine Romane: viii


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