Gell-Mann and low formula for degenerate unperturbed states

Annales Henri Poincare

Volumn 10, Issue 7, 2010, Pages 1285-1309

  Brouder, Christian ^a   Panati, Gianluca ^b   Stoltz, Gabriel ^c  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c UNIVERSITÉ PARIS EST   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 76649096315     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-009-0018-7     Document Type: Article

References (22)

1. Avron J. E., Seiler R., Yaffe L. G.: Adiabatic theorems and applications to the quantum Hall effect. Commun. Math. Phys. 110, 33-49 (1987).
2. Bloch C., Horowitz J.: Sur la détermination des premiers états d'un système de fermions dans le cas dégénéré. Nucl. Phys. 8, 91-97 (1958).
3. Born M., Fock V.: Beweis des Adiabatensatzes. Z. Phys. 51, 165-180 (1928).
4. Brouder C., Stoltz G., Panati G.: Adiabatic approximation, Gell-Mann and Low theorem and degeneracies: a pedagogical example. Phys. Rev. A 78, 042102 (2008).
5. Brouder C., Stoltz G., Panati G.: Many-body Green function of degenerate systems. Phys. Rev. Lett. 103, 230401 (2009).
6. Garrido L. M.: Generalized adiabatic invariance. J. Math. Phys. 5, 335-362 (1964).
7. Gell-Mann M., Low F.: Bound states in quantum field theory. Phys. Rev. 84(2), 350-354 (1951).
8. Hagedorn G. A.: Adiabatic expansions near eigenvalue crossings. Ann. Phys. 196, 278-295 (1989).
9. Hagedorn G. A., Joye A.: A time-dependent Born-Oppenheimer approximation with exponentially small error estimates. Commun. Math. Phys. 223(3), 583-626 (2001).
10. Hagedorn, G. A., Joye, A.: Mathematical analysis of Born-Oppenheimer approximations. In: Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday. Proceedings of the Symposium in Pure Mathematics, vol. 76, pp. 203-226. American Mathematical Society, Providence (2007).
11. Hirschfelder J. O.: Formal Rayleigh-Schrödinger perturbation theory for both degenerate and non-degenerate energy states. Int. J. Quantum Chem. 3, 731-748 (1969).
12. Kato T.: On the adiabatic theorem of quantum mechanics. J. Phys. Soc. Jpn. 5, 435-439 (1950).
13. Kato, T.: Perturbation theory for linear operators. Grundlehren der mathematischen Wissenschaften, vol. 132. Springer, Berlin (1976).
14. Martinez A., Sordoni V.: A general reduction scheme for the time-dependent Born-Oppenheimer approximation. C. R. Math. Acad. Sci. Paris 334(3), 185-188 (2002).
15. Nenciu G.: On the adiabatic theorem of quantum mechanics. J. Phys. A: Math. Gen. 13, L15-L18 (1980).
16. Nenciu G., Rasche G.: Adiabatic theorem and Gell-Mann & Low formula. Helvetica Phys. Acta 62, 372-388 (1989).
17. Panati G., Spohn H., Teufel S.: Space-adiabatic perturbation theory. Adv. Theor. Math. Phys. 7(1), 145-204 (2003).
18. Reed, M., Simon, B.: Fourier analysis and self-adjointness. In: Methods of Modern Mathematical Physics, vol. II. Academic Press, New York (1975).
19. Reed, M., Simon, B.: Analysis of operators. In: Methods of Modern Mathematical Physics, vol. IV. Academic Press, New York (1978).
20. Sakurai J. J.: Modern Quantum Mechanics. Addison-Wesley, Reading (1994).
21. Sjöstrand J.: Projecteurs adiabatiques du point de vue pseudodifférentiel. C. R. Acad. Sci. Paris Sér. I Math. 317(2), 217-220 (1993).
22. Teufel, S.: Adiabatic perturbation theory in quantum dynamics. In: Lecture Notes in Mathematics, vol. 1821. Springer, Berlin (2003).