Holomorphy of the Dirac resolvent with relatively form bounded potentials

Gregory B. White

Annales de l'I.H.P. Physique théorique (1993)

  • Volume: 59, Issue: 3, page 269-300
  • ISSN: 0246-0211

How to cite

top

White, Gregory B.. "Holomorphy of the Dirac resolvent with relatively form bounded potentials." Annales de l'I.H.P. Physique théorique 59.3 (1993): 269-300. <http://eudml.org/doc/76622>.

@article{White1993,
author = {White, Gregory B.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {power series expansion of the Dirac resolvent in a complex variable; potentials which are form bounded with respect to the momentum operator; Pauli-Schrödinger resolvent; Coulomb-like potentials; formable operators},
language = {eng},
number = {3},
pages = {269-300},
publisher = {Gauthier-Villars},
title = {Holomorphy of the Dirac resolvent with relatively form bounded potentials},
url = {http://eudml.org/doc/76622},
volume = {59},
year = {1993},
}

TY - JOUR
AU - White, Gregory B.
TI - Holomorphy of the Dirac resolvent with relatively form bounded potentials
JO - Annales de l'I.H.P. Physique théorique
PY - 1993
PB - Gauthier-Villars
VL - 59
IS - 3
SP - 269
EP - 300
LA - eng
KW - power series expansion of the Dirac resolvent in a complex variable; potentials which are form bounded with respect to the momentum operator; Pauli-Schrödinger resolvent; Coulomb-like potentials; formable operators
UR - http://eudml.org/doc/76622
ER -

References

top
  1. [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. Zbl0471.35024MR609226
  2. [De] P.A. Deift, Applications of a Commutation Formula, Duke Math. J., Vol. 45, 1978, pp. 267-310. Zbl0392.47013MR495676
  3. [DS] N. Dunford and J.T. Schwartz, Linear Operators, Part I, New York, Interscience, 1963. MR188745
  4. [F] W.G. Faris, Self-Adjoint Operators, Lecture Notes in Mathematics, Vol. 433, Berlin, Heidelberg, New York, Springer-Verlag, 1975. Zbl0317.47016MR467348
  5. [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. Zbl0039.22605
  6. [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. Zbl0534.46053MR747200
  7. [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. Zbl0705.35115MR1034588
  8. [H] W. Hunziker, On the Nonrelativistic Limit of the Dirac Theory, Commun. Math. Phys., Vol. 40, 1975, pp. 215-222. MR363275
  9. [K] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., New York, Berlin, Springer-Verlag, 1980. Zbl0435.47001
  10. [L] E. Lieb, The Stability of Matter: From Atoms to Stars, Bull. Am. Math. Soc., Vol, 22, No. 1, 1990, pp. 1-49. Zbl0698.35135MR1014510
  11. [M] A. Messiah, Quantum Mechanics, Vols. 1 & 2. Amsterdam: North Holland, 1970. 
  12. [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. Zbl0349.47014MR421456
  13. [RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vols. I, II, IV. New York, London, Academic Press1972-1978. MR493419
  14. [S] B. Simon, Quantum Mechanics for Hamiltonians Defined as Quadratic Forms: Princeton, New Jersey, Princeton University Press, 1971. Zbl0232.47053MR455975
  15. [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. Zbl0127.19004MR131598
  16. [V1] K. Veselic, Perturbation of Pseudoresolvents and Analyticity in 1/c of Relativistic Quantum Mechanics, Commun. Math. Phys., Vol. 22, 1971, pp. 27-43. Zbl0212.15701MR300579
  17. [V2] K. Veselic, The Nonrelativistic Limit of the Dirac Equation and the Spectral Concentration, Glasnik Mat., Vol. 4, 1969, pp. 231-241. Zbl0212.16402MR267294
  18. [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. Zbl0712.35082MR1077468

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.