Asymptotic completeness in quantum in field theory. Massive Pauli-Fierz Hamiltonians

Reviews in Mathematical Physics

Volumn 11, Issue 4, 1999, Pages 383-450

  Derezinski J ^a   Gerard C ^b  

^a UNIVERSITY OF WARSAW   (Poland)

^b CENTRE DE MATHÉMATIQUES LAURENT SCHWARTZ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038353790     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X99000155     Document Type: Article

References (50)

1. A. Arai, "On a model of a harmonic oscillator coupled to a quantized, massless, scalar field I.", J. Math. Phys. 22 (1981) 2539-2548.
2. A. Arai, "Self-adjointness and spectrum of Hamiltonians in non-relativistic quantum electrodynamics", J. Math. Phys. 22 (1981) 534-537.
3. A. Arai and M. Hirokawa, "On the existence and uniqueness of ground states of the spin-boson Hamiltonian", preprint, 1995.
4. D. Buchholz and K. Fredenhagen, "Collision theory for massless bosons", Commun. Math. Phys. 52 (1977) 147-176.
5. V. Bach, J. Fröhlich and I. Sigal, "Quantum electrodynamics of confined non-relativistic particles", Sonderforschungsbereich 288 preprint, 1996.
6. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Springer, Berlin, 1981.
7. J. C. Baez, I. E. Segal and Z. Zhou, Introduction to Algebraic and Constructive Quantum Field Theory, Princeton Univ. Press, Princeton, 1992.
8. P. Blanchard, Discussion mathematique du modèle de Pauli et Fierz relatif à la catastrophe infrarouge, Commun. Math. Phys. 15 (1969) 156-172.
9. C. Cohen-Tannoudji, J. Dupont-Roc and G. Grynberg, Photons and Atoms - Introduction to Quantum Electrodynamics, John Wiley, New York, 1991.
10. M. Combescure and F. Dunlop, "N-particle-irreducible functions in Euclidean quantum field theory", Ann. Phys. 122 (1979) 102-150.
11. E. B. Davies, "Markovian master equations", Commun. Math. Phys. 39 (1974) 91-110.
12. E. B. Davies, "Markovian master equations II", Math. Ann. 219 (1976) 147-158.
13. J. Dereziński and C. Gérard, Scattering Theory of Classical and Quantum N-Particle Systems, Texts and Monographs in Physics, Springer, 1997.
14. J. Dereziński, "Asymptotic completeness for N-particle long-range quantum systems", Ann. Math. 138 (1993) 427-476.
15. J. Dereziński, "Asymptotic completeness in quantum field theory. A class of Galilei-covariant models", preprint Ecole Polytechnique, 1996, to appear in Rev. Math. Phys.
16. V. Enss, "Long-range scattering of two-and three-body quantum systems, Journées "Equations aux dérivées partielles", Saint Jean de Monts, Juin 1989, Publications Ecole Polytechnique, Palaiseau, 1989.
17. K. O. Friedrichs, Perturbation of Spectra in Hilbert Space, AMS, Providence, 1965.
18. J. Fröhlich, "Existence of dressed one-electron states in a class of persistent models", Forschritte der Physik 22 (1974) 159-198.
19. J. Fröhlich, "On the infrared problem in a model of scalar electrons and massless scalar bosons", Ann. Inst. Henri Poincaré A19 (1973) 1-103.
20. R. Froese and I. Herbst, "A new proof of the Mourre estimate", Duke Math. J. 49 (1982) 1075-1085.
21. C. Gérard, "Asymptotic completeness for the spin-boson model with a particle number cutoff", Rev. Math. Phys. 8 (1996) 549-589.
22. 2 quantum field theory without cutoffs II. The field operators and the approximate vacuum", Ann. Math. 91 (1970) 362-401.
23. J. Glimm, and A. Jaffe, Quantum Physics. A Functional Integral Point of View, 2nd ed, Springer New York, Berlin, Heidelberg, 1987.
24. G. M. Graf, "Asymptotic completeness for N-body short range quantum systems: A new proof", Commun. Math. Phys. 132 (1990) 73-101.
25. R. Haag, Local Quantum Physics. Fields, Particles, Algebras, Springer, Berlin Heidelberg, 1992.
26. B. Helffer and J. Sjöstrand, "Equation de Schrödinger avec champ magnétique et equation de Harper", Springer Lecture Notes in Physics 345 (1989) 118-197.
27. H. Hepp, Theorie de la renormalisation, Berlin, Springer, 1968.
28. R. Høegh-Krohn, "Asymptotic limits in some models of quantum field theory, I", J. Math. Phys. 9 (1968) 2075-2079.
29. R. Høegh-Krohn, "Boson fields under a general class of cut-off interactions", Commun. Math. Phys. 12 (1969) 216-225.
30. R. Høegh-Krohn, "On the scattering matrix for quantum fields", Commun. Math. Phys. 18 (1970) 109-117.
31. M. Hübner and H. Spohn, "Radiative decay: Nonperturbative approaches", Rev. Math. Phys 7 (1995) 363-387.
32. M. Hübner and H. Spohn, "Spectral properties of the spin-boson Hamiltonian", Ann. Inst. H. Poincaré 62 (1995) 289-323.
33. D. Iagolnitzer, "Asymptotic completeness and multiparticle analysis in quantum field theories", Commun. Math. Phys. 110 (1987) 51.
34. V. Jaksic and C. A. Pillet, "On a model for quantum friction I: Fermi's golden rule at zero temperature", Ann. Inst. H. Poincaré (1995) 62-47.
35. V. Jaksic and C. A. Pillet, "On a model for quantum friction II: Fermi's golden rule and dynamics at zero temperature", Commun. Math. Phys. 176 (1995) 176-619.
36. V. Jaksic and C. A. Pillet, On a model for quantum friction III: Ergodic properties of the spin-boson system, to appear in Commun. Math. Phys.
37. H. Massen, "Return to equilibrium for the solution of quantum Langevin equation", J. Stat. Phys. 34 (1984) 239-261.
38. E. Mourre, "Absence of singular continuous spectrum for certain self-adjoint operators", Commun. Math. Phys. 78 (1981) 391-408.
39. E. Nelson, "Interaction of nonrelativistic particles with a quantized scalar field", J. Math. Phys. 5 (1964) 1190-1997.
40. T. Okamoto and K. Yajima, "Complex scaling technique in non-relativistic qed", Ann. Inst. H. Poincaré 42 (1985) 311-327.
41. W. Pauli and M. Fierz, Nuovo Cimento 15 (1938) 167.
42. M. Reed and B. Simon, Methods of Modern Mathematical Physics, vols. I and II, 1976, vol. III, 1979, vol. IV, 1978, Academic Press, London.
43. I. M. Sigal and A. Soffer, "The N-particle scattering problem: Asymptotic completeness for short-range quantum systems", Ann. Math. 125 (1987) 35-108.
44. 2 Euclidean (Quantum) Field Theory, Princeton Univ. Press, Princeton, 1974.
45. E. Skibsted, "Spectral analysis of N-body systems coupled to a bosonic system", preprint, 1997.
46. H. Spohn, "Ground states of the spin-boson hamiltonian", Commun. Math. Phys. 123 (1989) 277-304.
47. H. Spohn, "Asymptotic completeness for Raleigh scattering", preprint, 1996.
48. H. Spohn, "Ground state of a quantum particle coupled to a scalar Bose field", preprint IHES, 1997.
49. S. Weinberg, The Quantum Theory of Fields, vol. I, Cambridge Univ. Press, 1995.
50. D. R. Yafaev, "Radiation conditions and scattering theory for N-particle hamiltonians", Commun. Math. Phys. 154 (1993) 523-554.