Puits multiples pour l'opérateur de Dirac
Wang, Xue Ping
Annales de l'I.H.P. Physique théorique, Tome 43 (1985), p. 269-319 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPA_1985__43_3_269_0,
     author = {Wang, Xue Ping},
     title = {Puits multiples pour l'op\'erateur de Dirac},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {43},
     year = {1985},
     pages = {269-319},
     mrnumber = {824842},
     zbl = {0614.35074},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPA_1985__43_3_269_0}
}

Wang, Xue Ping. Puits multiples pour l'opérateur de Dirac. Annales de l'I.H.P. Physique théorique, Tome 43 (1985) pp. 269-319. http://gdmltest.u-ga.fr/item/AIHPA_1985__43_3_269_0/

[1] R. Abraham, J. Marsden, Foundations of Mechanics, 2nd Ed., Benjamin, Cumming Publ. Company, 1978. | MR 515141 | Zbl 0393.70001

[2] S. Agmon, Lectures on exponential decay of solutions of second order elliptic equations, Math. Notes, t. 29, Princeton University Press, 1982. | MR 745286 | Zbl 0503.35001

[3] A.M. Berthier, V. Georgescu, Sur le spectre ponctuel de l'opérateur de Dirac. C. R. Acad. Sci. Paris, t. 297, 1983, Série I, p. 335-338. | MR 732500 | Zbl 0546.35052

[4] R. Chernoff, Schrödinger and Dirac operators with singular potentials and hyperbolic equations, Pac. J. Math., t. 72 (2), 1977, p. 361-383. | MR 510049 | Zbl 0366.35031

[5] J.M. Combes, P. Duclos, R. Seiler, Krein's formula and one dimensional multiple well, J. Funct. Anal., t. 52, 1983, p. 257-301. | MR 707207 | Zbl 0562.47002

[6] J.M. Combes, P. Duclos, R. Seiler, Convergent Expansion for Tunneling, Comm. Math. Phys., t. 92, 1982, p. 229-245. | MR 728868 | Zbl 0579.47050

[7] E.M. Harrell, Double Well, Comm. Math. Phys., t. 75, 1980, p. 239-261. | MR 581948 | Zbl 0445.35036

[8] E.M. Harrell, M. Klaus, On the double-well problem for Dirac operators, Ann. Inst. Henri Poincaré, t. 38 (2), 1983, p. 153-166. | Numdam | MR 705337 | Zbl 0529.35062

[9] B. Helffer, D. Robert, Calcul fonctionnel par la transformation de Mellin et applications, J. Funct. Anal., t. 53 (3), 1983, p. 245-268. | Zbl 0524.35103

[10] B. Helffer, D. Robert, Puits de potentiel généralisés et asymptotique semi-classique, Ann. Inst. Henri Poincaré, Sect. A, t. 41, 1984, p. 291-332. | Numdam | MR 776281 | Zbl 0565.35082

[11] B. Helffer, J. Sjöstrand, Multiple wells in the semi-classical limit I, Comm. P. D. E., t. 9 (4), 1984, p. 337-408. | MR 740094 | Zbl 0546.35053

[12] B. Helffer, J. Sjöstrand, Puits multiples et limites semi-classique II. Interaction moléculaire, symétries, perturbation, Ann. Inst. Henri Poincaré, section Phys. Théorique, t. 42, 1985, p. 127-212. | Numdam | MR 798695 | Zbl 0595.35031

[13] B. Helffer, J. Sjöstrand, Multiple wells in the semi-classical limi III. Interaction through non-resonnant wells, à paraître Mathematisch Nachrichte. | Zbl 0597.35023

[14] M. Klaus, On the point spectrum of Dirac operators, Helv. Phys. Acta, t. 53, 1980, p. 453-462. | MR 611769

[15] M. Klaus, R. Wüst, Spectral properties of Dirac operators with singular potentials, J. Math. Anal. and Appl., t. 72, 1979, 206-214. | MR 552332 | Zbl 0423.47014

[16] J. Leray, Analyse Lagrangienne, Collège de France, 1976-1977. | MR 501198

[17] J. Leray, Solution Asymptotique de l'équation de Dirac, in Trends in Applications of Pure Mathematics to Mechanics, Pitman, 1976, p. 233-240. | Zbl 0346.35092

[18] V.P. Maslov, M.V. Fedoriuk, Semi-classical Approximation in Quantum Mechanics, D. Reidel, 1981. | Zbl 0458.58001

[19] B. Müller, W. Greiner, The two centre Dirac equation; Z. Naturforsch., t. 30 (1), 1976, p. 1-30.

[20] J.C. Nosmas, Approximation Semi-classique du spectre de systèmes asymptotiques, C. R. Acad. Sci. Paris, t. 295, 1982, p. 253-256. | Zbl 0535.58040

[21] D. Robert, Calcul fonctionnel sur les opérateurs admissibles et application, J. Funct. Anal., t. 45 (1), 1982, p. 74-94. | MR 645646 | Zbl 0482.35069

[22] D. Robert, Autour de l'Approximation Semi-classique, Notas de Curso, N° 21, Universidada Federal de Pernambuco, Recife, 1983.

[23] J.P. Serre, Représentations Linéaires des Groupes Finis, Hermann, Paris, 1967. | MR 232867 | Zbl 0189.02603

[24] B. Simon, Semi-classical analysis of low lying eigenvalues, I. Non-degenerate minima: Asymptotic expansions, Ann. Inst. Henri Poincaré, t. 38, 1983, p. 295- 307. | Numdam | MR 708966 | Zbl 0526.35027

[25] B. Simon, Semi-classical analysis of low lying eigenvalues, II. Tunneling, Ann. of Math., t. 120, 1984, p. 89-118. | MR 750717 | Zbl 0626.35070

[26] X.P. Wang, Asymptotic behavior of spectral means of pseudo-differential operators, J. of Appr. Theory and Appl., t. 1, 1985, p. 119-136. | MR 816606 | Zbl 0595.47036

[27] E. Witten, Fermion Quantum Numbers in Kaluza-Klein Theory, prétirage.

[28] K. Yajima, The quasi-classical approximation to Dirac equation, I. J. Fac. Sci. Univ. Tokyo, t. 29, 1982, p. 161-194. | Zbl 0486.35075