@article{AIHPA_1989__51_3_231_0, author = {Grigore, D. R. and Nenciu, Gheorghe and Purice, R.}, title = {On the nonrelativistic limit of the Dirac hamiltonian}, journal = {Annales de l'I.H.P. Physique th\'eorique}, volume = {51}, year = {1989}, pages = {231-263}, mrnumber = {1034588}, zbl = {0705.35115}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPA_1989__51_3_231_0} }
Grigore, D. R.; Nenciu, G.; Purice, R. On the nonrelativistic limit of the Dirac hamiltonian. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) pp. 231-263. http://gdmltest.u-ga.fr/item/AIHPA_1989__51_3_231_0/
[1] Kvantovaja elektrodinamics, Gosudarstvennoe izdatel' stvo fiziko-matematicskoj literatury, Moscova, 1959.
and ,[2] Spectral Properties of Schrödinger Operators and Scattering Theory, Ann. Sc. Sup. Pisa, Vol. 2, 1975, pp. 151-218. | Numdam | MR 397194 | Zbl 0315.47007
,[3] Scattering Theory in Quantum Mechanics, W. A. Benjamin Inc., Reading Massachusetts, 1977. | MR 495999 | Zbl 0376.47001
, and ,[4] Some Generalization of the Foldy-Wouthuysen Transformation, Phys. Rev., Vol. 95, 1954, pp. 1323-1328. | MR 66971 | Zbl 0057.20601
,[5] Existence du Temps de Retard en Théorie de la Diffusion Quantique Non-Relativiste, Thèse, Univ. de Genève, 1987.
,[6] Foldy-Wouthuysen Transformations and Related Problems, Fortschr. f. Physik, Vol. 18, 1970, pp. 149-182.
,[7] Foldy-Wouthuysen Transformation; Exact Solution with Generalization to the two-Particle Problem, Phys. Rev., Vol. 111, 1958, pp. 1011-1016. | MR 95054 | Zbl 0082.41705
,[8] Canonical Transformations of Dirac's Equation to Even Forms. Expansion in Terms of the External Fields, Nuovo Cim., Suppl. 18, 1960, pp. 1- 39. | MR 128843
and ,[9] On the Dirac Theory of Spin 1/2 Particles and its Nonrelativistic limit, Phys. Rev., Vol. 78, 1950, pp. 29-36. | Zbl 0039.22605
and ,[10] A Rigorous Approach to Relativistic Corrections of Bound State Energies for Spin -1/2 Particles, Ann. Inst. H. Poincaré, Vol. 40, 1984, p. 159. | Numdam | MR 747200 | Zbl 0534.46053
, and ,[11] On the Spectra of Schrödinger Multiparticle Hamiltonians, Helv. Phys. Acta, Vol. 39, 1966, pp. 451-462. | MR 211711 | Zbl 0141.44701
,[12] On the Nonrelativistic Limit of the Dirac Theory, Comm. Math. Phys., Vol. 40, 1975, pp. 215-222. | MR 363275
,[13] Spectral Properties of Schrödinger Operators and Time-decay of the Wave Functions, Duke Math. J., Vol. 46, 1979, pp. 583-612. | MR 544248 | Zbl 0448.35080
and ,[14] Perturbation Theory for Linear Operators, 2nd ed., Springer Verlag, New York, Berlin, 1980. | MR 407617
,[15] Scattering Theory for Differential Operators I: Operator Theory, J. Math. Soc. Japan, Vol. 25, 1973, pp. 75-104. | MR 326435 | Zbl 0245.47006
,[16] Scattering Theory for Differential Operators II: Self-Adjoint Elliptic Operators, J. Math. Soc. Japan, Vol. 25, 1973, pp. 222-234. | MR 326436 | Zbl 0252.47007
,[17] IV, 2e Parite, Ed. Mir, Moscou, 1972.
and , Physique Théorique; Vol.[18] Eigenfunction Expansions for Schrödinger and Dirac Operators with Singular Potentials, Comm. Math. Phys., Vol. 42, 1975, pp. 221-229. | MR 374705 | Zbl 0326.35064
,[19] Existence of the Spontaneous Pair Creation in the External Field Approximation of Q.E.D., Comm. Math. Phys., Vol. 109, 1987, pp. 303-312. | MR 880417 | Zbl 0627.58040
,[20] 43, 1927, p. 601. | JFM 53.0858.02
, Z. f. Phys., Vol.[21] Relativistic Potential Scattering, J. Math. Phys., Vol. 4, 1963, p. 1048. | MR 154563 | Zbl 0128.22004
,[22] Scattering Theory for Elliptic Operators of Arbitrary Order, Comm. Math. Helv., Vol. 49, 1974, pp. 84-113. | MR 367484 | Zbl 0288.47012
,[23] An Introduction to Relativistic Quantum Field Theory. New York, Harper & Row Publishers Inc., 1961. | Zbl 0111.43102
,[24] Normal Forms of an Abstract Dirac Operator and Applications to Scattering Theory, J. Math. Phys., Vol. 29, 1988, pp. 249-257. | MR 921790 | Zbl 0639.47043
,[25] Perturbation of Pseudoresolvents and Analyticity in 1/c of Relativistic Quantum Mechanics, Comm. Math. Phys., Vol. 22, 1971, pp. 27-43. | MR 300579 | Zbl 0212.15701
,[26] Nonrelativistic Limit of the Dirac Theory, Scattering Theory, J. Fac. Sci., Univ. of Tokyo I A, Vol. 23, 1976, pp. 517-523. | MR 434240 | Zbl 0341.47001
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