@article{AIHPA_1990__53_1_109_0, author = {White, Gregory B.}, title = {Splitting of the Dirac operator in the nonrelativistic limit}, journal = {Annales de l'I.H.P. Physique th\'eorique}, volume = {52}, year = {1990}, pages = {109-121}, mrnumber = {1077468}, zbl = {0712.35082}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPA_1990__53_1_109_0} }
White, Gregory B. Splitting of the Dirac operator in the nonrelativistic limit. Annales de l'I.H.P. Physique théorique, Tome 52 (1990) pp. 109-121. http://gdmltest.u-ga.fr/item/AIHPA_1990__53_1_109_0/
[1] Dirac and Klein-Gordon Equations: Convergence of solutions in the nonrelativistic limit, Commun. Math. Phys., Vol. 79, 1981, pp. 33-46. | MR 609226 | Zbl 0471.35024
and ,[2] Asymptotic analysis of some abstract evolution equations, J. Funct. Anal., Vol. 25, 1977, pp. 81-101. | MR 451031 | Zbl 0347.47021
,[3] Applications of a commutation formula, Duke Math J., Vol. 45, 1978, pp. 267-310. | MR 495676 | Zbl 0392.47013
,[4] On the Dirac theory of spin 1/2 particles and its non-relativistic limit, Phys. Rev., Vol. 78, 1950, pp. 29-36. | Zbl 0039.22605
and ,[5] A rigorous approach to relastivistic corrections of bound state energies for spin-1/2 particles, Ann. Inst. Henri Poincaré, Vol. 40, No. 2, 1984, pp. 159-174. | Numdam | MR 747200 | Zbl 0534.46053
, and ,[6] First-Order Relastivic Correlations and Spectral Concentration, Adv. Appl. Math., Vol. 6, 1985, pp. 159-176. | MR 789851 | Zbl 0595.47007
, and ,[7] Functional Analysis and Semigroups, Am. Math. Soc. Colloquium Publications XXXI, Providence, R. I., 1957. | MR 89373 | Zbl 0078.10004
and ,[8] On the nonrelativistic limit of the Dirac theory, Commun. Math. Phys., Vol. 40, 1975, pp. 215-222. | MR 363275
,[9] Perturbation Theory for Linear Operators, 2nd ed., Springer-Verlag, New York/Berlin, 1980.
,[10] 1 & 2, North Holland, Amsterdam, 1970. | Zbl 0102.42602
, Quantum Mechanics, Vols.[11] Relativistic Potential Scattering, J. Math. Phys., Vol. 4, 1964, pp. 1048-1054. | MR 154563 | Zbl 0128.22004
,[12] I: Functional Analysis, Academic Press, New York/London, 1972. | Zbl 0242.46001
and , Methods of Modern Mathematical Physics, Vol.[13] II: Fourier Analysis/Self-Adjointness, Academic Press, New York/London, 1975. | Zbl 0308.47002
and , Methods of Modern Mathematical Physics, Vol.[14] IV: Analysis of Operators, Academic Press, New York/London, 1978. | Zbl 0401.47001
and , Methods of Modern Mathematical Physics, Vol.[15] Relativistic Electron Theory, John Wiley & Sons, Inc., New York/London, 1961. | Zbl 0096.43905
[16] Perturbation of pseudoresolvents and analyticity in 1/c of relativistic quantum mechanics, Commun. Math. Phys., 22, 1971, pp. 27-43. | MR 300579 | Zbl 0212.15701
,[17] The nonrelativistic limit of the Dirac operator: Splitting of the operator and classification of the discrete spectrum, Ph. D. Thesis, University of California, Los Angeles, 1988.
,