@article{AIHPA_1989__51_3_231_0, author = {Grigore, D. R. and Nenciu, G. and Purice, R.}, title = {On the nonrelativistic limit of the {Dirac} hamiltonian}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {231--263}, publisher = {Gauthier-Villars}, volume = {51}, number = {3}, year = {1989}, mrnumber = {1034588}, zbl = {0705.35115}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1989__51_3_231_0/} }
TY - JOUR AU - Grigore, D. R. AU - Nenciu, G. AU - Purice, R. TI - On the nonrelativistic limit of the Dirac hamiltonian JO - Annales de l'I.H.P. Physique théorique PY - 1989 SP - 231 EP - 263 VL - 51 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1989__51_3_231_0/ LA - en ID - AIHPA_1989__51_3_231_0 ER -
Grigore, D. R.; Nenciu, G.; Purice, R. On the nonrelativistic limit of the Dirac hamiltonian. Annales de l'I.H.P. Physique théorique, Volume 51 (1989) no. 3, pp. 231-263. http://www.numdam.org/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 | Zbl
,[3] Scattering Theory in Quantum Mechanics, W. A. Benjamin Inc., Reading Massachusetts, 1977. | MR | Zbl
, and ,[4] Some Generalization of the Foldy-Wouthuysen Transformation, Phys. Rev., Vol. 95, 1954, pp. 1323-1328. | MR | Zbl
,[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 | Zbl
,[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
and ,[9] On the Dirac Theory of Spin 1/2 Particles and its Nonrelativistic limit, Phys. Rev., Vol. 78, 1950, pp. 29-36. | Zbl
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 | Zbl
, and ,[11] On the Spectra of Schrödinger Multiparticle Hamiltonians, Helv. Phys. Acta, Vol. 39, 1966, pp. 451-462. | MR | Zbl
,[12] On the Nonrelativistic Limit of the Dirac Theory, Comm. Math. Phys., Vol. 40, 1975, pp. 215-222. | MR
,[13] Spectral Properties of Schrödinger Operators and Time-decay of the Wave Functions, Duke Math. J., Vol. 46, 1979, pp. 583-612. | MR | Zbl
and ,[14] Perturbation Theory for Linear Operators, 2nd ed., Springer Verlag, New York, Berlin, 1980. | MR
,[15] Scattering Theory for Differential Operators I: Operator Theory, J. Math. Soc. Japan, Vol. 25, 1973, pp. 75-104. | MR | Zbl
,[16] Scattering Theory for Differential Operators II: Self-Adjoint Elliptic Operators, J. Math. Soc. Japan, Vol. 25, 1973, pp. 222-234. | MR | Zbl
,[17] Physique Théorique; Vol. IV, 2e Parite, Ed. Mir, Moscou, 1972.
and ,[18] Eigenfunction Expansions for Schrödinger and Dirac Operators with Singular Potentials, Comm. Math. Phys., Vol. 42, 1975, pp. 221-229. | MR | Zbl
,[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 | Zbl
,[20] Z. f. Phys., Vol. 43, 1927, p. 601. | JFM
,[21] Relativistic Potential Scattering, J. Math. Phys., Vol. 4, 1963, p. 1048. | MR | Zbl
,[22] Scattering Theory for Elliptic Operators of Arbitrary Order, Comm. Math. Helv., Vol. 49, 1974, pp. 84-113. | MR | Zbl
,[23] An Introduction to Relativistic Quantum Field Theory. New York, Harper & Row Publishers Inc., 1961. | Zbl
,[24] Normal Forms of an Abstract Dirac Operator and Applications to Scattering Theory, J. Math. Phys., Vol. 29, 1988, pp. 249-257. | MR | Zbl
,[25] Perturbation of Pseudoresolvents and Analyticity in 1/c of Relativistic Quantum Mechanics, Comm. Math. Phys., Vol. 22, 1971, pp. 27-43. | MR | Zbl
,[26] Nonrelativistic Limit of the Dirac Theory, Scattering Theory, J. Fac. Sci., Univ. of Tokyo I A, Vol. 23, 1976, pp. 517-523. | MR | Zbl
,