Crossed products of C*-algebras and spectral analysis of quantum hamiltonians

Communications in Mathematical Physics

Volumn 228, Issue 3, 2002, Pages 519-560

  Georgescu, Vladimir ^a   Iftimovici, Andrei ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036022814     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200200669     Document Type: Article

References (37)

1. Baaj, S., Julg, P.: Théorie bivariante de Kasparov et opérateurs non bornés dans les C*-modules hilbertiens. C.R. Acad. Sci. Paris 296, 875-878 (1983)
2. Beals, R.: Characterization of pseudodifferential operators and applications. Duke Math. J. 44, no. 1, 45-57 (1977)
3. Bellissard, J.: K-Theory of C*-algebras in Solid State Physics. In: Dorlas, T.C., Hugenholtz, N.M., Winnink, M. (eds.), Statistical Mechanics and Field Theory: Mathematical Aspects, Groningen 1985, Lecture Notes in Physics 257, 1986, pp. 99-156
4. Bellissard, J.: Gap Labelling Theorems for Schrödinger Operators. In: Luck, J.M., Moussa, P., Waldschmidt, M. (eds.). From Number Theory to Physics, Les Houches 1989, Springer Proceedings in Physics 47, Berlin-Heidelberg-New York: Springer, 1993, pp. 538-630
5. Bellissard, J.: Non-Commutative Methods in Semiclassical Analysis. In Bellissard, J. et al. (eds.) Transition to Chaos in Classical and Quantum Mechanics, CIME Montecatini Terme 1991, Lecture Notes in Mathematics, 1589, Berlin-Heidelberg-New York: Springer, 1994, pp. 2-60
6. Bellissard, J.,van Elst, A., Schulz-Baldes, H.: The noncommutative geometry of the quantum Hall effect. Topology and physics. J. Math. Phys. 35, no. 10, 5373-5451 (1994)
7. Benbernou, M.: Spectral analysis of the acoustic propagator in a multistratified domain. J. Math. Anal. Appl. 225, no. 2, 440-460 (1998)
8. Carey, A.L., Hannabuss, K.C., Mathai, V., McCann, P.: Quantum Hall effect on the hyperbolic plane. Commun. Math. Phys. 190, no. 3, 629-673 (1998)
9. Cordes, H.O.: Spectral theory of linear differential operators and comparison algebras. Cambridge: Cambridge University Press, 1987
10. Croc, E., Iftimie, V.: Wave operators in a multistratified strip. Integral Equations Operator Theory 33, no. 4, 389-405 (1999)
11. Cycon, H.L., Froese, R.G., Kirsch, W., Simon, B.: Schrödinger operators, with applications to quantum mechanics and global geometry. Berlin-Heidelberg-New York: Springer-Verlag, 1987
12. Damak, M., Georgescu, V.: C*-crossed products and a generalized quantum mechanical N-body problem. Electronic J. of Diff. Equations, Conference 04 (Proceedings of the symposium "Mathematical Physics and Quantum Field Theory"), 51-69 (2000) (an improved version is available as preprint 99-481 at http://www.ma.utexas.edu/mp_arc/)
13. Damak, M., Georgescu, V.: C*-algebras related to the N-body problem and the self-adjoint operators affiliated to them. Preprint 99-482 at http://www.ma.utexas.edu/mp_arc/
14. Davidson, K.R.: C*-algebras by example, Fields institute monographs 6, American Mathematical Society, 1996
15. Dereziński, J., Gérard, C.: Spectral and scattering theory of spatially cut-off P(φ)2 hamiltonians. Commun. Math. Physics 213, no. 1, 39-125 (2000)
16. Dermenjian, Y., Durand, M., Iftimie, V.: Spectral analysis of an acoustic multistratified perturbed cylinder. Comm. Partial Differential Equations 23, no. 1-2, 141-169 (1998)
17. Dixmier, J.: Les C*-algebres et leurs représentations, 2e ed., Gauthier-Villars, 1969
18. Folland, G.B.: A Course in abstract harmonic analysis. CRC Press, 1995
19. Folland, G.B.: Harmonic analysis in phase space. Annals of Mathematics Studies 122, Princeton University press, 1989
20. Georgescu, V.: Spectral analysis of quantum field models with a particle number cutoff. In Demuth, M., Schultze B.-W. (eds.) Partial Differential Equations and Spectral Theory. Proceedings, Clausthal 2000, pp. 139-147, Operator Theory: Advances and Applications 126, Birkhäuser Verlag, 2001
21. Georgescu, V., Iftimovici, A.: The Riesz-Kolmogorov and Ruelle criteria on locally compact abelian groups. Preprint 00-520 at http://www.ma.utexas.edu/mp_arc/
22. Georgescu, V., Iftimovici, A.: C*-algebras of energy observables: I. General theory and bumps algebras. Preprint 01-521 at http://www.ma.utexas.edu/mp_arc/
23. Georgescu, V., Iftimovici, A.: C*-algebras of energy observables: II. Graded symplectic algebras and magnetic hamiltonians. Preprint 01-99 at http://www.ma.utexas.edu/mp_arc/
24. Helffer, B., Mohamed, A.: Caractérisation du spectre essentiel de l'Opérateur de Schrödinger avec un champ magnétique. Ann. Inst. Fourier, Grenoble 38, 95-112 (1988)
25. Hundertmark, D., Kirsch, W.: Spectral theory of sparse potentials. Preprint 00-217 at http://mpej.unige.ch/mp_arc/
26. Iftimovici, A.: Nonperturbative techniques in the investigation of the spectral properties of many-channel systems. In: Demuth, M., Schultze, B.-W. (eds.), Partial Differential Equations and Spectral Theory. Proceedings, Clausthal 2000, Operator Theory: Advances and Applications 126, Birkhäuser Verlag, 2001, pp. 155-163
27. 2 + V where V has infinitely many "bumps". Ann. Inst. H. Poincaré Sect. A (N.S.) 38, no. 1, 7-13 (1983)
28. Lagarias, J.C., Pleasants, P.A.B.: Repetitive Delone sets and quasicristals. Preprint at http://www.research.att.com/̃jcl/papers.html
29. Lance, E.C.: Hilbert C*-modules: a toolkit for operator algebraists. Cambridge: Cambridge University Press, 1995
30. Mǎntoiu, M.: On a class of anisotropic Schrodinger operators Preprint 01-201 at http://www.ma.utexas.edu/mp_arc/
31. Mǎntoiu, M.: C*-algebras, dynamical systems at infinity and the essential spectrum of generalized Schrodinger operators. Preprint 01-298 at http://www.ma.utexas.edu/mp_arc/
32. Murphy, G.J.: C*-algebras and operator theory. London: Academic Press, 1990
33. Pearson, D.B.: Singular continuous measures in scattering theory. Commun. Math. Phys. 60, no. 1, 13-36 (1978)
34. Pedersen, G.K.: C*-algebras and their automorphisms groups. London: Academic Press, 1979
35. Takai, H.: On a duality for crossed products of C*-algebras. J. Funct. Anal. 19, 25-39 (1975)
36. Woronowicz, S.L.: Unbounded elements affiliated with C*-algebras and non-compact quantum groups. Commun. Math. Phys. 136, 399-432 (1991)
37. Woronowicz, S.L., Napiórkowski, K.: Operator theory in the C*-algebra framework. Rep. Math. Phys. 31, 353-371 (1992)