Essential spectrum of a self-adjoint operator on an abstract Hilbert space of Fock type and applications to quantum field hamiltonians

Journal of Mathematical Analysis and Applications

Volumn 246, Issue 1, 2000, Pages 189-216

  Arai, Asao ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

Essential spectrum; Fock space; second quantization; quantum field; spin boson model; Pauli Fierz model

Indexed keywords

EID: 0034195732     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.6782     Document Type: Article

References (27)

1. Amrein W. O., Jauch J. M., Sinha K. B. Scattering Theory in Quantum Mechanics. 1977;Benjamin, Reading.
2. Arai A. Perturbation of embedded eigenvalues: A general class of exactly soluble models in Fock spaces. Hokkaido Math. J. 19:1990;1-34.
3. Arai A. An abstract sum formula and its applications to special functions. J. Math. Anal. Appl. 167:1992;245-265.
4. Arai A. On the Essential Spectra of Quantum Field Hamiltonians. Hokkaido University Preprint Series in Mathematics. 426:1998.
5. Arai A., Hirokawa M. On the existence and uniqueness of ground states of a generalized spin-boson model. J. Funct. Anal. 151:1997;455-503.
6. Arai A., Hirokawa M., Hiroshima F. On the Absence of Eigenvectors of Hamiltonians in a Class of Massless Quantum Field Models without Infrared Cutoff. J. Funct. Anal. 168:1999;470-497.
7. Bach V., Fröhlich J., Sigal I. M. Quantum electrodynamics of confined nonrelativistic particles. Adv. Math. 137:1998;299-395.
8. V. Bach, J. Fröhlich, and, I. M. Sigal, Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field, preprint, 1998.
9. de Monvel A. Boutet, Sahbani J. On the spectral properties of the spin-boson Hamiltonians. Lett. Math. Phys. 44:1998;22-33.
10. J. Dereziński, and, V. Jakšić, Spectral Theory of Pauli-Fierz Hamiltonians I, preprint, 1998.
11. Fefferman C., Fröhlich J., Graf G. M. Stability of ultraviolet-cutoff quantum electrodynamics with non-relativistic matter. Comm. Math. Phys. 190:1997;309-330.
12. Gérard C. Asymptotic completeness for the spin-boson model with a particle number cutoff. Rev. Math. Phys. 8:1996;549-589.
13. 2 quantum field theory without cutoffs. II. The field operators and the approximate vacuum. Ann. of Math. 91:1970;362-401.
14. F. Hiroshima, Ground States and Spectrum of Quantum Electrodynamics of Non-relativistic Particles, preprint, 1998.
15. Høegh-Krohn R. On the spectrum of the space cut-off: P(φ): Hamiltonian in two space-time dimensions. Comm. Math. Phys. 21:1971;256-260.
16. Hübner M., Spohn H. Spectral properties of the spin-boson Hamiltonian. Ann. Inst. Henri Poincaré 62:1995;289-323.
17. Jakšić V., Pillet C.-A. On a model for a quantum friction. I. Fermi's golden rule and dynamics at zero temperature. Ann. Inst. Henri Poincaré 62:1995;47-68.
18. Jakšić V., Pillet C.-A. On a model for a quantum friction. II. Fermi's golden rule and dynamics at positive temperature. Comm. Math. Phys. 176:1996;619-644.
19. Kato Y., Mugibayashi N. Asymptotic fields in model field theories. Progr. Theoret. Phys. 45:1971;628-639.
20. Nelson E. Interaction of nonrelativistic particles with a quantized scalar field. J. Math. Phys. 5:1964;1190-1197.
21. Okamoto T., Yajima K. Complex scaling technique in non-relativistic massive QED. Ann. Inst. Henri Poincaré 42:1985;311-327.
22. Pauli W., Fierz M. Zur Theorie der Emission langwelliger Lichtquanten. Nuovo Cimento. 15:1938;167-188.
23. Reed M., Simon B. Methods of Modern Mathematical Physics I: Functional Analysis. 1972;Academic Press, New York.
24. Reed M., Simon B. Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness. 1975;Academic Press, New York.
25. Reed M., Simon B. Methods of Modern Mathematical Physics IV: Analysis of Operators. 1978;Academic Press, New York.
26. Skibsted E. Spectral analysis of N-body systems coupled to a bosonic field. Rev. Math. Phys. 10:1998;989-1026.
27. Spohn H. Ground state of a quantum particle coupled to a scalar Bose field. Lett. Math. Phys. 44:1998;9-16.