Splitting of the Dirac operator in the nonrelativistic limit

Gregory B. White

Annales de l'I.H.P. Physique théorique (1990)

  • Volume: 53, Issue: 1, page 109-121
  • ISSN: 0246-0211

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White, Gregory B.. "Splitting of the Dirac operator in the nonrelativistic limit." Annales de l'I.H.P. Physique théorique 53.1 (1990): 109-121. <http://eudml.org/doc/76491>.

@article{White1990,
author = {White, Gregory B.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Dirac operator; Pauli-Schrödinger operators; spectral gap; separation of the electron and positron energy levels},
language = {eng},
number = {1},
pages = {109-121},
publisher = {Gauthier-Villars},
title = {Splitting of the Dirac operator in the nonrelativistic limit},
url = {http://eudml.org/doc/76491},
volume = {53},
year = {1990},
}

TY - JOUR
AU - White, Gregory B.
TI - Splitting of the Dirac operator in the nonrelativistic limit
JO - Annales de l'I.H.P. Physique théorique
PY - 1990
PB - Gauthier-Villars
VL - 53
IS - 1
SP - 109
EP - 121
LA - eng
KW - Dirac operator; Pauli-Schrödinger operators; spectral gap; separation of the electron and positron energy levels
UR - http://eudml.org/doc/76491
ER -

References

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  1. [1] 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. Zbl0471.35024MR609226
  2. [2] E.B. Davies, Asymptotic analysis of some abstract evolution equations, J. Funct. Anal., Vol. 25, 1977, pp. 81-101. Zbl0347.47021MR451031
  3. [3] P.A. Deift, Applications of a commutation formula, Duke Math J., Vol. 45, 1978, pp. 267-310. Zbl0392.47013MR495676
  4. [4] 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. Zbl0039.22605
  5. [5] F. Gesztesy, H. Grosse and B. Thaller, 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. Zbl0534.46053MR747200
  6. [6] F. Gesztesy, H. Grosse and B. Thaller, First-Order Relastivic Correlations and Spectral Concentration, Adv. Appl. Math., Vol. 6, 1985, pp. 159-176. Zbl0595.47007MR789851
  7. [7] E. Hille and R. Phillips, Functional Analysis and Semigroups, Am. Math. Soc.Colloquium Publications XXXI, Providence, R. I., 1957. Zbl0078.10004MR89373
  8. [8] W. Hunziker, On the nonrelativistic limit of the Dirac theory, Commun. Math. Phys., Vol. 40, 1975, pp. 215-222. MR363275
  9. [9] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer-Verlag, New York/Berlin, 1980. Zbl0435.47001
  10. [10] A. Messiah, Quantum Mechanics, Vols. 1 & 2, North Holland, Amsterdam, 1970. Zbl0102.42602
  11. [11] R. Prosser, Relativistic Potential Scattering, J. Math. Phys., Vol. 4, 1964, pp. 1048-1054. Zbl0128.22004MR154563
  12. [12] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. I: Functional Analysis, Academic Press, New York/London, 1972. Zbl0242.46001
  13. [13] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. II: Fourier Analysis/Self-Adjointness, Academic Press, New York/London, 1975. Zbl0308.47002
  14. [14] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. IV: Analysis of Operators, Academic Press, New York/London, 1978. Zbl0401.47001
  15. [15] M.E. RoseRelativistic Electron Theory, John Wiley & Sons, Inc., New York/London, 1961. Zbl0096.43905
  16. [16] K. Veselič, Perturbation of pseudoresolvents and analyticity in 1/c of relativistic quantum mechanics, Commun. Math. Phys., 22, 1971, pp. 27-43. Zbl0212.15701MR300579
  17. [17] G.B. White, 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. 

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