Limiting absorption principle for the Dirac operator
Anne Boutet de Monvel-Berthier; Dragos Manda; Radu Purice
Annales de l'I.H.P. Physique théorique (1993)
- Volume: 58, Issue: 4, page 413-431
- ISSN: 0246-0211
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topBoutet de Monvel-Berthier, Anne, Manda, Dragos, and Purice, Radu. "Limiting absorption principle for the Dirac operator." Annales de l'I.H.P. Physique théorique 58.4 (1993): 413-431. <http://eudml.org/doc/76612>.
@article{BoutetdeMonvel1993,
author = {Boutet de Monvel-Berthier, Anne, Manda, Dragos, Purice, Radu},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {limiting absorption principle; spectrum of the Dirac Hamiltonian; long- range potentials; Coulombian singularities; non-local potentials},
language = {eng},
number = {4},
pages = {413-431},
publisher = {Gauthier-Villars},
title = {Limiting absorption principle for the Dirac operator},
url = {http://eudml.org/doc/76612},
volume = {58},
year = {1993},
}
TY - JOUR
AU - Boutet de Monvel-Berthier, Anne
AU - Manda, Dragos
AU - Purice, Radu
TI - Limiting absorption principle for the Dirac operator
JO - Annales de l'I.H.P. Physique théorique
PY - 1993
PB - Gauthier-Villars
VL - 58
IS - 4
SP - 413
EP - 431
LA - eng
KW - limiting absorption principle; spectrum of the Dirac Hamiltonian; long- range potentials; Coulombian singularities; non-local potentials
UR - http://eudml.org/doc/76612
ER -
References
top- [1] W.O. Amrein, A. Boutet De MONVEL-BERTHIER and V. Georgescu, Notes on the N-body problem, I, preprint de l'Université de Genève, UGVA-DPT1988/11-598 a, 1988, pp. 1-156.
- [2] E. Balslev and B. Helffer, Limiting absorption principle and resonances for the Dirac operator, Advances to Applied Mathematics, 1991 (to appear). Zbl0756.35062MR1243034
- [3] J. Bergh and J. Löfström, Interpolation spaces: an introduction, Springer-Verlag, 1976. Zbl0344.46071MR482275
- [4] A. Boutet de Monvel-Berthier and V. Georgescu, Locally conjugate operators, boundary values of the resolvent and Wave Operators, C. R. Acad. Sci. Paris, Tome 313, Series I, 1991, pp. 13-18. Zbl0733.47026MR1115939
- [5] A. Boutet de Monvel-Berthier and V. Georgescu, Spectral and scattering theory by the conjugate operator method, Algebra and Analysis, Vol. 4, 3, 1992, pp. 73-116 ( = St. Petersburg J., 1992) and Universität Bielefeld, BiBoS, preprint n° 477/91. Zbl0791.47010MR1190772
- [6] A. Boutet de Monvel-Berthier, V. Georgescu and M. Mantoiu, Locally smooth operators and the limiting absorption principle for N body hamiltonians, Reviews in Math. Phys., Vol. 5, 1, 1993, pp. 1-90 and Universität Bielefeld, BiBoS, preprint n° 433/1990. Zbl0806.47063MR1219531
- [7] A. Boutet de Monvel-Berthier, D. Manda and R. Purice, The commutator method for form-relatively compact perturbations, Letters in Math. Physics, Vol. 22, 1991, pp. 211-223. Zbl0752.35042MR1129176
- [8] E.B. Davies, One parameter semigroups, Academic Press, 1980. Zbl0457.47030MR591851
- [9] W. Faris, Self-adjoint operators, Lecture Notes in Math., 433, Springer, 1975. Zbl0317.47016MR467348
- [10] C. Itzykson and J.B. Zuber, Quantum field theory, Mc Graw-Hill, 1980. Zbl0453.05035MR585517
- [11] T. Kato, Perturbations of linear operators, Springer-Verlag, 1966. Zbl0148.12601
- [12] T. Kato and K. Yajima, Dirac equation with moving nuclei, Ann. Inst. H. Poincaré, Vol. 54, (2), 1991, pp. 209-221. Zbl0748.35033MR1110653
- [13] E. Mourre, Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math. Phys., Vol. 78, 1981, pp. 391-408. Zbl0489.47010MR603501
- [14] E. Mourre, Opérateurs conjugués et propriétés de propagation, Comm. Math. Phys., Vol. 91, 1983, pp. 279-300. Zbl0543.47041MR723552
- [15] G. Nenciu, Distinguished self-adjoint extensions for Dirac operator with potential dominated by multicenter Coulomb potentials, Helv. Phys. Acta, Vol. 50, 1977, pp. 1-3. MR462346
- [16] P. Perry, I. Sigal and B. Simon, Spectral analysis for N-body operators, Ann. Math., Vol. 114, 1981, p. 519-567. Zbl0477.35069MR634428
- [17] M. Reed and B. Simon, Methods of modern mathematical Physics, Vol. II, Academic Press, New York, 1975.
- [18] M. Reed and B. Simon, Methods of modern mathematical Physics, Vol. IV, Academic Press, New York, 1978.
- [19] B. Simon, Quantum mechanics for Hamiltonians defined as quadratic forms, Princeton University Press, 1971. Zbl0232.47053MR455975
- [20] B. Thaller and V. Enss, Asymptotic observables and Coulomb scattering for the Dirac equation, Ann. Inst. H. Poincaré, Vol. 45, (2), 1986, pp. 147-171. Zbl0615.47008MR866913
- [21] V. Vogelsang, Remark on essential self-adjointness of Dirac operators with Coulomb Potentials, Math. Z., Vol. 196, 1987, pp. 517-521. Zbl0617.35127MR917234
- [22] V. Vogelsang, Self-adjoint extensions of Dirac operators with non spherically symmetric potentials in Coulomb scattering, Int. Eq. and Op. Theor., Vol. 10, 1987, pp. 841-858. Zbl0643.47028
- [23] V. Vogelsang, Absolutely continuous spectrum of Dirac operators for long-range potentials, J. Func. Anal., Vol. 76, 1988, pp. 67-86. Zbl0652.47030MR923045
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