Ground states of a model in nonrelativistic quantum electrodynamics. I

Journal of Mathematical Physics

Volumn 40, Issue 12, 1999, Pages 6209-6222

  Hiroshima, Fumio ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033249084     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533087     Document Type: Article

References (26)

1. F. Hiroshima, "Ground states of a model in nonrelativistic quantum electrodynamics. II," J. Math. Phys. (to be published).
2. W. Pauli and M. Fierz, "Zur Theorie der Emission langwelliger Lichtquanten," Nuovo Cimento 15, 167-188 (1938).
3. H. A. Bethe, "The electromagnetic shift of energy levels," Phys. Rev. 72, 339-342 (1947).
4. T. A. Welton, "Some observable effects of the quantum mechanical fluctuations of the electromagnetic field," Phys. Rev. 74, 1157-1169 (1948).
5. A. Arai, "An asymptotic analysis and its application to the nonrelativistic limit of the Pauli-Fierz and a spin-boson model," J. Math. Phys. 31, 2653-2663 (1990).
6. F. Hiroshima, "Scaling limit of a model in quantum electrodynamics," J. Math. Phys. 34, 4478-4518 (1993).
7. F. Hiroshima, "Scaling limit of a model in quantum electrodynamics with many nonrelativistic particles," Rev. Math. Phys. 9, 201-225 (1997).
8. A. Arai, "Self-adjointness and spectrum of Hamiltonians in nonrelativistic quantum electrodynamics," J. Math. Phys. 22, 534-537 (1981).
9. A. Arai, "On a model of a harmonic oscillator coupled to a quantized, massless scalar field I," J. Math. Phys. 22, 2539-2548 (1981).
10. A. Arai, "Rigorous theory of spectra and radiation for a model in quantum electrodynamics," J. Math. Phys. 24, 1896-1910 (1983).
11. V. Bach, J. Fröhlich, and I. M. Sigal, "Quantum electrodynamics of confined nonrelativistic particles," Adv. Math. 137, 299-395 (1998).
12. C. Fefferman, "On electrons and nuclei in a magnetic field," Adv. Math. 124, 100-153 (1996).
13. C. Fefferman, J. Fröhlich, and G. M. Graf, "Stability of ultraviolet-cutoff quantum electrodynamics with nonrelativistic matter," Commun. Math. Phys. 190, 309-330 (1997).
14. F. Hiroshima, "Ground states and spectrum of quantum electrodynamics of nonrelativistic particles" (preprint).
15. A. Amman, "Ground states of a spin-boson models," Ann. Phys. 208, 414-448 (1991).
16. A. Arai and M. Hirokawa, "On the existence and uniqueness of the ground states of a generalized spin-boson model," J. Funct. Anal. 151, 455-503 (1997).
17. J. Fröhlich, "Existence of dressed one electron states in a class of persistent models," Fortschr. Phys. 22, 159-198 (1974).
18. H. Spohn, "Ground state(s) of the spin-boson Hamiltonian," Commun. Math. Phys. 123, 277-304 (1989).
19. H. Spohn, "Ground state of quantum particle coupled to a scalar boson field," Lett. Math. Phys. 44, 9-16 (1998).
20. 2 quantum field theory without cutoffs II. The field operators and approximate vacuum," Ann. Math. 91, 362-401 (1970).
21. M. Reed and B. Simon, Method of Modern Mathematical Physics (Academic, New York, 1974), Vol. II.
22. T. Okamoto and K. Yajima, "Complex scaling technique in nonrelativistic massive QED," Ann. Inst. Henri Poincaré 42, 311-327 (1985).
23. F. Hiroshima, "Essential self-adjointness of translation-invariant quantum field models for arbitrary coupling constants" (preprint).
24. B. Simon and Hrøegh-Krohn, "Hypercontractive semigroup and two-dimensional self-coupled Bose fields," J. Funct. Anal. 9, 121-180 (1972).
25. V. Bach, J. Fröhlich, and I. M. Sigal, "Spectral analysis for systems of atoms and molecules coupled to the quantized radiation field" (preprint).
26. A. Arai, M. Hirokawa, and F. Hiroshima, "On the absence of eigenvectors of Hamiltonians in a class of massless quantum field models without infrared cutoff," J. Funct. Anal. (to be published).