Holomorphy of the Dirac resolvent with relatively form bounded potentials
White, Gregory B.
Annales de l'I.H.P. Physique théorique, Tome 59 (1993), p. 269-300 / Harvested from Numdam
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@article{AIHPA_1993__59_3_269_0,
     author = {White, Gregory B.},
     title = {Holomorphy of the Dirac resolvent with relatively form bounded potentials},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {59},
     year = {1993},
     pages = {269-300},
     mrnumber = {1276327},
     zbl = {0791.47057},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1993__59_3_269_0}
}

White, Gregory B. Holomorphy of the Dirac resolvent with relatively form bounded potentials. Annales de l'I.H.P. Physique théorique, Tome 59 (1993) pp. 269-300. http://gdmltest.u-ga.fr/item/AIHPA_1993__59_3_269_0/

[CC] R.J. Cirincione and P.R. Chernoff, 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

[De] P.A. Deift, Applications of a Commutation Formula, Duke Math. J., Vol. 45, 1978, pp. 267-310. | MR 495676 | Zbl 0392.47013

[DS] N. Dunford and J.T. Schwartz, Linear Operators, Part I, New York, Interscience, 1963. | MR 188745

[F] W.G. Faris, Self-Adjoint Operators, Lecture Notes in Mathematics, Vol. 433, Berlin, Heidelberg, New York, Springer-Verlag, 1975. | MR 467348 | Zbl 0317.47016

[FW] L.L. Foldy and S.A. Wouthuysen, 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

[GGT] F. Gesztesy, H. Grosse and B. Thaller, A Rigorous Approach to Relativistic Corrections of Bound State Energies for Spin-1/2 Particles, Ann. I.H.P. (Phys. Théor.), Vol. 40, 1984, pp. 159-174. | Numdam | MR 747200 | Zbl 0534.46053

[GNP] D.R. Grigore, G. Nenciu and R. Purice, On the Nonrelativistic Limit of the Dirac Hamiltonian, Ann. I.H.P. (Phys. Théor.), Vol. 51, 1989, pp. 231-263. | Numdam | MR 1034588 | Zbl 0705.35115

[H] W. Hunziker, On the Nonrelativistic Limit of the Dirac Theory, Commun. Math. Phys., Vol. 40, 1975, pp. 215-222. | MR 363275

[K] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., New York, Berlin, Springer-Verlag, 1980.

[L] E. Lieb, The Stability of Matter: From Atoms to Stars, Bull. Am. Math. Soc., Vol, 22, No. 1, 1990, pp. 1-49. | MR 1014510 | Zbl 0698.35135

[M] A. Messiah, Quantum Mechanics, Vols. 1 & 2. Amsterdam: North Holland, 1970.

[N] G. Nenciu, Self-Adjointness and Invariance of the Essential Spectrum for Dirac Operators Defined as Quadratic Forms, Comm. Math. Phys., Vol. 48, 1976, pp. 235-247. | MR 421456 | Zbl 0349.47014

[RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vols. I, II, IV. New York, London, Academic Press 1972-1978. | MR 493419 | Zbl 0242.46001

[S] B. Simon, Quantum Mechanics for Hamiltonians Defined as Quadratic Forms: Princeton, New Jersey, Princeton University Press, 1971. | MR 455975 | Zbl 0232.47053

[T] E.C. Titchmarsh, On the Relation between the Eigenvalues in Relativistic and Nonrelativistic Quantum Mechanics, Proc. Roy. Soc., Vol. A 266, 1962, pp. 33-46. | MR 131598 | Zbl 0127.19004

[V1] K. Veselic, Perturbation of Pseudoresolvents and Analyticity in 1/c of Relativistic Quantum Mechanics, Commun. Math. Phys., Vol. 22, 1971, pp. 27-43. | MR 300579 | Zbl 0212.15701

[V2] K. Veselic, The Nonrelativistic Limit of the Dirac Equation and the Spectral Concentration, Glasnik Mat., Vol. 4, 1969, pp. 231-241. | MR 267294 | Zbl 0212.16402

[W] G.B. White, Splitting of the Dirac Operator in the Nonrelativistic Limit, Ann. I.H.P. (Phys. Théor.), Vol. 53, 1990, pp. 109-121. | Numdam | MR 1077468 | Zbl 0712.35082