Singular Quadratic Forms in Perturbation Theory

Volodymyr Koshmanenko (Autor)

Buch | Hardcover

312 Seiten

1999 | 1999 ed.
Springer (Verlag)
978-0-7923-5625-7 (ISBN)

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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(

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.

Reihe/Serie	Mathematics and Its Applications ; 474
Reihe/Serie	Mathematics and Its Applications ; 474
Zusatzinfo	VIII, 312 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	170 x 244 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
ISBN-10	0-7923-5625-X / 079235625X
ISBN-13	978-0-7923-5625-7 / 9780792356257
Zustand	Neuware