Ground state and resonances in the standard model of the non-relativistic QED

Journal of Statistical Physics

Volumn 134, Issue 5-6, 2009, Pages 899-939

  Sigal, Israel Michael ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Non relativistic QED; Quantum electro dynamics; Renormalization group; Resonances; Spectrum ground state

Indexed keywords

EID: 67349228223     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9721-5     Document Type: Article

References (59)

1. Abou Salem, W., Faupin, J., Frohlich, J., Sigal, I.M.: On theory of resonances in non-relativistic QED. Adv. Appl. Math. (2009, to appear)
2. Amour, L., Grbert, B., Guillot, J.-C.: The dressed mobile atoms and ions. J. Math. Pures Appl. (9) 86(3), 177-200 (2006)
3. Arai, A.: Mathematical analysis of a model in relativistic quantum electrodynamics. In: Applications of Renormalization Group Methods in Mathematical Sciences, Kyoto (1999) (in Japanese)
4. Arai, A., Hirokawa, M.: Ground states of a general class of quantum field Hamiltonians. Rev. Math. Phys. 12(8), 1085-1135 (2000)
5. Bach, V., Chen, T., Fröhlich, J., Sigal, I.M.: Smooth Feshbach map and operator-theoretic renormalization group methods. J. Funct. Anal. 203, 44-92 (2003)
6. Bach, V., Chen, T., Fröhlich, J., Sigal, I.M.: The renormalized electron mass in non-relativistic quantum electrodynamics. J. Funct. Anal. 243, 426-535 (2007)
7. Bach, V., Fröhlich, J., Pizzo, A.: Infrared-finite algorithms in QED: the groundstate of an atom interacting with the quantized radiation field. Commun. Math. Phys. 264(1), 145-165 (2006)
8. Bach, V., Fröhlich, J., Pizzo, A.: An infrared-finite algorithm for Rayleigh scattering amplitudes, and Bohr's frequency condition. Commun. Math. Phys. 274(2), 457-486 (2007)
9. Bach, V., Fröhlich, J., Pizzo, A.: Infrared-Finite Algorithms in QED II. The Expansion of the Groundstate of an Atom Interacting with the Quantized Radiation Field, mp-arc
10. Bach, V., Fröhlich, J., Sigal, I.M.: Mathematical theory of non-relativistic matter and radiation. Lett. Math. Phys. 34, 183-201 (1995)
11. Bach, V., Fröhlich, J., Sigal, I.M.: Quantum electrodynamics of confined non-relativistic particles. Adv. Math. 137, 299-395 (1998)
12. Bach, V., Fröhlich, J., Sigal, I.M.: Renormalization group analysis of spectral problems in quantum field theory. Adv. Math. 137, 205-298 (1998)
13. Bach, V., Fröhlich, J., Sigal, I.M.: Spectral analysis for systems of atoms and molecules coupled to the quantized radiation field. Commun. Math. Phys. 207(2), 249-290 (1999)
14. Bach, V., Fröhlich, J., Sigal, I.M., Soffer, A.: Positive commutators and spectrum of Pauli-Fierz Hamiltonian of atoms and molecules. Commun. Math. Phys. 207(3), 557-587 (1999)
15. Berger, M.: Nonlinearity and Functional Analysis. Lectures on Nonlinear Problems in Mathematical Analysis. Pure and Applied Mathematics. Academic Press, New York (1977)
16. Catto, I., Exner, P., Hainzl, Ch.: Enhanced binding revisited for a spinless particle in nonrelativistic QED. J. Math. Phys. 45(11), 4174-4185 (2004)
17. Catto, I., Hainzl, C.: Self-energy of one electron in non-relativistic QED. J. Funct. Anal. 207(1), 68-110 (2004)
18. Chen, T.: Infrared renormalization in non-relativistic QED and scaling criticality. J. Funct. Anal. 254(10), 2555-2647 (2008)
19. Chen, T., Fröhlich, J., Pizzo, A.: Infraparticle scattering states in non-relativistic QED, I: the Bloch-Nordsieck paradigm. arXiv:0709.2493
20. Chen, T., Fröhlich, J., Pizzo, A.: Infraparticle scattering states in non-relativistic QED, II: mass shell properties. arXiv:0709.2812
21. Cohen-Tannoudji, C., Dupont-Roc, J., Grynberg, G.: Photons and Atoms-Introduction to Quantum Electrodynamics. Wiley, New York (1991)
22. Cohen-Tannoudji, C., Dupont-Roc, J., Grynberg, G.: Atom-Photon Interactions-Basic Processes and Applications. Wiley, New York (1992)
23. Faupin, J.: Resonances of the confined hydrogenoid ion and the Dicke effect in non-relativistic quantum electrodynamics. Ann. H. Poincaré 9(4), 743-773 (2008)
24. Fröhlich, J., Griesemer, M., Schlein, B.: Asymptotic completeness for Compton scattering. Commun. Math. Phys. 252(1-3), 415-476 (2004)
25. Fröhlich, J., Griesemer, M., Sigal, I.M.: Spectral theory for the standard model of non-relativistic QED. Commun. Math. Phys. 283(3), 613-646 (2008)
26. Fröhlich, J., Griesemer, M., Sigal, I.M.: Spectral renormalization group analysis. e-print, ArXiv (2008)
27. Fröhlich, J., Griesemer, M., Sigal, I.M.: Spectral renormalization group and limiting absorption principle for the standard model of non-relativistic QED. In preparation
28. Griesemer, M.: Non-relativistic matter and quantized radiation. e-print, arXiv
29. Griesemer, M., Hasler, D.: On the smooth Feshbach-Schur map. J. Funct. Anal. 254(9), 2329-2335 (2008)
30. Griesemer, M., Hasler, D.: Analytic perturbation theory and renormalization analysis of matter coupled to quantized radiation. arXiv:0801.4458
31. Griesemer, M., Lieb, E.H., Loss, M.: Ground states in non-relativistic quantum electrodynamics. Invent. Math. 145(3), 557-595 (2001)
32. Gustafson, S., Sigal, I.M.: Mathematical Concepts of Quantum Mechanics, 2nd edn. Springer, Berlin (2006)
33. Hainzl, Ch.: One non-relativistic particle coupled to a photon field. Ann. H. Poincaré 4(2), 217-237 (2003)
34. Hainzl, Ch., Seiringer, R.: Mass renormalization and energy level shift in non-relativistic QED. Adv. Theor. Math. Phys. 6(5), 847-871 (2003)
35. Hasler, D., Herbst, I.: Absence of ground states for a class of translation invariant models of non-relativistic QED. Commun. Math. Phys. 279(3), 769-787 (2008)
36. Hasler, D., Herbst, I., Huber, M.: On the lifetime of quasi-stationary states in non-relativistic QED. Ann. H. Poincaré 9(5), 1005-1028 (2008). arXiv:0709.3856
37. Hille, E., Phillips, R.S.: Functional Analysis and Semi-Groups. AMS, Reading (1957)
38. Hirokawa, M.: Recent developments in mathematical methods for models in non-relativistic quantum electrodynamics. In: A Garden of Quanta, pp. 209-242. World Scientific, River Edge (2003)
39. Hiroshima, F.: Ground states of a model in nonrelativistic quantum electrodynamics, I. J. Math. Phys. 40(12), 6209-6222 (1999)
40. Hiroshima, F.: Ground states of a model in nonrelativistic quantum electrodynamics, II. J. Math. Phys. 41(2), 661-674 (2000)
41. Hiroshima, F.: Ground states and spectrum of quantum electrodynamics of nonrelativistic particles. Trans. Am. Math. Soc. 353(11), 4497-4528 (2001) (electronic)
42. Hiroshima, F.: Self-adjointness of the Pauli-Fierz Hamiltonian for arbitrary values of coupling constants. Ann. H. Poincaré 3(1), 171-201 (2002)
43. Hiroshima, F.: Nonrelativistic QED at large momentum of photons. In: A Garden of Quanta, pp. 167-196. World Scientific, River Edge (2003)
44. Hiroshima, F.: Analysis of ground states of atoms interacting with a quantized radiation field. In: Topics in the Theory of Schrödinger Operators, pp. 145-272. World Scientific, River Edge (2004)
45. Hiroshima, F., Spohn, H.: Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin. Adv. Theor. Math. Phys. 5(6), 1091-1104 (2001)
46. Hiroshima, F., Spohn, H.: Mass renormalization in nonrelativistic quantum electrodynamics. J. Math. Phys. 46(4) (2005)
47. Hislop, P., Sigal, I.M.: Introduction to Spectral Theory. Applications to Schrödinger Operators. Applied Mathematical Sciences, vol. 113. Springer, New York (1996)
48. Hunziker, W.: Resonances, metastable states and exponential decay laws in perturbation theory. Commun. Math. Phys. 132(1), 177-188 (1990)
49. Hunziker, W., Sigal, I.M.: The quantum N-body problem. J. Math. Phys. 41(6), 3448-3510 (2000)
50. Kato, T.: Perturbation Theory of Linear Operators. Grundlehren der mathematischen Wissenschaften, vol. 132, 2 edn. Springer, Berlin (1976)
51. King, Ch.: Resonant decay of a two state atom interacting with a massless non-relativistic quantized scalar field. Commun. Math. Phys. 165(3), 569-594 (1994)
52. Lieb, E.H., Loss, M.: Existence of atoms and molecules in non-relativistic quantum electrodynamics. Adv. Theor. Math. Phys. 7, 667-710 (2003). arXiv:math-ph/0307046
53. Lieb, E.H., Loss, M.: Self-energy of electrons in non-perturbative QED. In: Conference Mosh Flato 1999, vol. I, Dijon. Math. Phys. Stud., vol. 21, pp. 327-344. Kluwer Academic, Dordrecht (2000)
54. Lieb, E.H., Loss, M.: A bound on binding energies and mass renormalization in models of quantum electrodynamics. J. Stat. Phys. 108 (2002)
55. Loss, M., Miyao, T., Spohn, H.: Lowest energy states in nonrelativistic QED: Atoms and ions in motion J. Funct. Anal. 243(2), 353-393 (2007)
56. Mück, M.: Construction of metastable states in quantum electrodynamics. Rev. Math. Phys. 16(1), 1-28 (2004)
57. Pizzo, A.: Scattering of an infraparticle: the one particle sector in Nelson's massless model. Ann. H. Poincaré 6(3), 553-606 (2005)
58. Reed, M., Simon, B.: Methods of Modern Mathematical Physics, IV, Analysis of Operators. Academic Press, New York (1978)
59. Spohn, H.: Dynamics of Charged Particles and Their Radiation Field. Cambridge University Press, Cambridge (2004)