Skip to main content
SpringerLink
Log in

Folgerungen aus der Diracschen Theorie des Positrons

  • Chapter
Original Scientific Papers / Wissenschaftliche Originalarbeiten

Part of the book series: Gesammelte Werke / Collected Works ((1853,volume A / 2))

Zusammenfassung

Aus der Diracschen Theorie des Positrons folgt, da jedes elektromagnetische Feld zur Paarerzeugung neigt, eine Abänderung der Maxwellschen Gleichungen des Vakuums. Diese Abänderungen werden für den speziellen Fall berechnet, in dem keine wirklichen Elektronen und Positronen vorhanden sind, und in dem sich das Feld auf Strecken der Compton-Wellenlänge nur wenig ändert.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. See W. Heisenberg: Der Teil und das Ganze (Piper Verlag, Munich 1969), especially p. 131; in English: Physics and Beyond (A.J. Pomerans, transl., Harper and Row, New York 1971 ), p. 92.

    Google Scholar 

  2. See the Annotation to the papers of Group 3 in Gesammelte Werke/Collected Works A I, pp. 329 — 343.

    Google Scholar 

  3. W. Heisenberg: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172–198 (1927); reprinted as paper No. 3.7 in Gesammelte Werke/ Collected Works A I, pp. 478 — 504

    Google Scholar 

  4. N. Bohr: Nature 121, 580 (1928)

    Article  MATH  Google Scholar 

  5. P.A.M. Dirac: Proc. R. Soc. London A 117, 610 (1928)

    Article  MATH  Google Scholar 

  6. P.A.M. Dirac: Proc. R. Soc. London A 118, 351 (1928)

    Article  MATH  Google Scholar 

  7. Ref. [5], p. 618

    Google Scholar 

  8. P.A.M. Dirac: Phys. Z. 29, 561, 712 (1928)

    Google Scholar 

  9. Wolfgang Pauli: Wissenschaftlicher Briefwechsel/Scientific Correspondence, Volume I: 1919–1929 ( Springer-Verlag, New York, Heidelberg, Berlin 1979 )

    Google Scholar 

  10. See the Annotation to the papers of Group 4 in Gesammelte Werke/Collected Works A I, pp. 507–515.

    Google Scholar 

  11. See Ref. [8], p. 562, footnote 2.

    Google Scholar 

  12. W. Heisenberg, letter to W. Pauli, July 31, 1928; published in Scientific Correspondence I, Ref. [9], p. 467

    Google Scholar 

  13. A date refers to the time of receipt by a journal of a paper in question.

    Google Scholar 

  14. H. Weyl: Z. Phys. 56, 332 (1929)

    Google Scholar 

  15. P.A.M. Dirac: Proc. R. Soc. London A 126, 360 (1929); Nature 126126, 605 (1930)

    MATH  Google Scholar 

  16. H. Weyl: The Theory of Groups and Quantum Mechanics (H.P. Robertson, transi., Methuen and Co., London 1931) pp. 263–264 and Preface

    Google Scholar 

  17. R. Oppenheimer: Phys. Rev. 35, 562 (1930); I. Tamm: Z. Phys. 62, 545 (1930)

    Google Scholar 

  18. P.A.M. Dirac: Proc. R. Soc. London A 133, 60 (1931)

    Article  Google Scholar 

  19. C.D. Anderson: Science 76, 238 (1932); Phys. Rev. 43, 491 (1933)

    Article  Google Scholar 

  20. See the Annotations of Group 10 in this volume and of Groups 12 and 13 in Volume AIII.

    Google Scholar 

  21. R. Oppenheimer: Phys. Rev. 35, 461 (1930)

    Article  MATH  Google Scholar 

  22. I. Waller: Z. Phys. 62, 673 (1930)

    Article  MATH  Google Scholar 

  23. V. Weisskopf: Z. Phys. 89, 27 (1934); V. Weisskopf (and W. Furry): Z. Phys. 90, 817 (1934)

    Google Scholar 

  24. H.B.G. Casimir: Z. Phys. 81, 496 (1933)

    Article  Google Scholar 

  25. C.N. Yang, D. Feldman: Phys. Rev. 79, 972 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  26. G. Källén: Ark. Fys. 89, 187, 371 (1950)

    Google Scholar 

  27. W. Heisenberg, letter to Pauli, July 21, 1933; published in Wolfgang Pauli: Wissenschaftlicher Briefwechsel/Scientific Correspondence, Volume II: 1930–1939 (Springer-Verlag, Berlin, Heidelberg 1985 ) pp. 206, 207

    Google Scholar 

  28. W. Pauli, letter to W. Heisenberg, September 24, 1933; published in Scientific Correspondence II, Ref. [27]. p. 212

    Google Scholar 

  29. P.A.M. Dirac: in Structure et Propriétés des Noyaux Atomiques. Rapports et Discussions du Septième Conseil de Physique ( Gauthier-Villars, Paris 1934 ) p. 203

    Google Scholar 

  30. At about that time W.H. Furry and J.R. Oppenheimer independently made the same calculation: Phys. Rev. 45, 245 (1934); see especially their footnote 11. R. Peierls also did similar work: Proc. R. Soc. London A146, 420 (1934).

    Google Scholar 

  31. A numerical error in his coefficient of the second term has been corrected.

    Google Scholar 

  32. E.A. Uehling: Phys. Rev. 48, 55 (1935)

    Article  MATH  Google Scholar 

  33. R. Serber: Phys. Rev. 48, 49 (1935)

    Article  Google Scholar 

  34. P.A.M. Dirac: Proc. Cambridge Philos. Soc. 30, 150 (1934)

    Google Scholar 

  35. W. Pauli, letter to W. Heisenberg, February 6, 1934; published in Scientific Correspondence II, Ref. [27], p. 277

    Google Scholar 

  36. W. Heisenberg, letter to W. Pauli, February 8, 1934; published in Scientific Correspondence II, Ref. [27], p. 279

    Google Scholar 

  37. W. Heisenberg, letter to W. Pauli, Aprii 25, 1935; published in Scientific Correspondence II, Ref. [27], p. 386

    Google Scholar 

  38. W. Pauli, letter to W. Heisenberg, June 14, 1934; published in Scientific Correspondence II, Ref. [27], p. 327

    Google Scholar 

  39. W. Pauli, letter to W. Heisenberg, January 21, 1934; published in Scientific Correspondence II, Ref. [27], p. 354

    Google Scholar 

  40. W. Pauli, V. Weisskopf: Helv. Phys. Acta 7, 709 (1934).In those times, Pauli’s attitude to the Dirac theory showed a marked ambivalence. In June 1934, he wrote about the theory of spinning electrons as “my old enemy” (meine alte Feindin). In 1935, he spoke of the Pauli-Weisskopf theory as the “anti-Dirac theory”: in The Theory of the Positron and Related Topics. Report of a Seminar Conducted by W. Pauli, notes by B. Hoffmann (The Institute of Advanced Study, Princeton, NJ, 1935–1936), unpublished.

    Google Scholar 

  41. For the case of no interaction, this formulation was also advocated by V. Fock: Dokl. Akad. Nauk 1, 267 (1933).

    Google Scholar 

  42. W. Pauli, letter to W. Heisenberg, December 11, 1933; published in Scientific Correspondence II, Ref. [27], p. 238

    Google Scholar 

  43. The first self-energy calculation O(e2) with the help of Heisenberg’s new method was in fact completed in March 1934, in Zürich [23], where Heisenberg’s ideas had been known since the previous December.

    Google Scholar 

  44. The density matrix approach was put into modern language in a series of papers by J.G. Valatin: Proc. R. Soc. London A222, 93, 228 (1954); A225, 535 (1954); A226, 254 (1954). More recently, off-diagonal distances have made their appearance in operator product expansions, see e.g., K.G. Wilson, W. Zimmermann: Commun. Math. Phys. 24, 87 (1971).

    Google Scholar 

  45. R. Serber: Phys. Rev. 49, 545 (1936)

    Article  Google Scholar 

  46. M. Born, W. Heisenberg, P. Jordan: Ober Quantenmechanik. II. Z. Phys. 35, 557–615 (1926); reprinted as paper No. 3.4 in Gesammelte Werke/Collected Works A I, pp. 397–455

    Google Scholar 

  47. A. Pais: Subtle is the Lord: The Science and the Life of Albert Einstein, (Oxford University Press, Oxford 1982) Chap. 21

    Google Scholar 

  48. Cf. J.J. Gonzales, H. Wergeland: K. -Nor. Vidensk. Selsk. Skr. No. 4 (1973)

    Google Scholar 

  49. Heisenberg discussed only the case b h/mc. The case b i h/mc was treated by R. Jost, J. Lut-tinger: unpublished; cf. also E. Corinaldesi: Nuovo Cim. 8, 494 (1951); Suppl. Nuovo Cimento 10, 83 (1953); W. Pauli: Selected Topics in Field Quantization (MIT Press, Cambridge, MA 1973 ) pp. 41, 42.

    Google Scholar 

  50. W. Heisenberg, letter to W. Pauli, March 22, 1935; published in Scientific Correspondence II, Ref. [27], pp. 381–382

    Google Scholar 

  51. W. Heisenberg, letter to W. Pauli, April 25, 1935; published in Scientific Correspondence II, Ref. [27] p. 386

    Google Scholar 

  52. O. Halpern: Phys. Rev. 44, 855 (1933)

    Article  Google Scholar 

  53. H. Euler, B. Kockel: Die Naturwissenschaften 23, 246 (1935); cf. also N. Kemmer, V. Weisskopf: Nature 137, 659 (1936)

    Google Scholar 

  54. Many more details are given in Euler’s doctoral thesis: Ann. Phys. (5) 26, 398 (1936). For A i h/mc one has a -(e2/hc)°d2, a result first obtained by A. Achieser: Phys. Z. Sowjetunion 11, 263 (1937).

    Google Scholar 

  55. This paper also contains a few corrections to paper No. 4.

    Google Scholar 

  56. Their calculations were simplified shortly afterwards by V. Weisskopf: K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 14, No. 6 (1936).

    Google Scholar 

  57. Of less interest is the comparison they made between the pair-induced nonlinearities and those contained in the still-born nonlinear electrodynamics of M. Born, L. Infeld: Proc. R. Soc. London A 143, 410 (1933); M. Born, L. Infeld: Proc. R. Soc. London A 144, 425 (1934); A 147, 522 (1934); A150, 141 (1935).

    Google Scholar 

  58. H.A. Kramers: Nuovo Cimento 15, 108 (1938)

    Article  MATH  Google Scholar 

  59. W. Heisenberg, letter to W. Pauli, June 8, 1934; published in Scientific Correspondence II, Ref. [27], p. 326. See also Ref. [51].

    Google Scholar 

  60. W. Heisenberg, letter to W. Pauli, May 23, 1936; published in Scientific Correspondence II, Ref. [27], p. 443

    Google Scholar 

  61. W. Heisenberg, letter to W. Pauli, December 14, 1957

    Google Scholar 

  62. Most of these letters have meanwhile been published in Wolfgang Pauli: Wissenschaftlicher Briefwechsel/Scientific Correspondence II. See Ref. [27].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Leipzig, Deutschland

    W. Heisenberg & H. Euler

Authors
  1. W. Heisenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Euler
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Max-Planck-Institut für Physik und Astrophysik, Werner-Heisenberg-Institut für Physik, Föhringer Ring 6, D-8000, München 40, Fed. Rep. of Germany

    Walter Blum , Hans-Peter Dürr  & Helmut Rechenberg ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Heisenberg, W., Euler, H. (1989). Folgerungen aus der Diracschen Theorie des Positrons. In: Blum, W., Dürr, HP., Rechenberg, H. (eds) Original Scientific Papers / Wissenschaftliche Originalarbeiten. Gesammelte Werke / Collected Works, vol A / 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70078-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-70078-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-52241-3

  • Online ISBN: 978-3-642-70078-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation