Advertisement

Heisenberg and Pauli: Their Program of a Unified Quantum Field Theory of Elementary Particles (1927–1958)

  • Helmut Rechenberg
Part of the Gesammelte Werke / Collected Works book series (HEISENBERG, volume A / 3)

Abstract

Heisenberg got to know Wolfgang Pauli soon after starting his studies at the University of Munich in fall 1920. He recalled [1]:

When I walked into the hall where Sommerfeld usually gave his lectures, I spotted a dark-haired student with a somewhat secretive face in the third row. Sommerfeld had introduced us during my first visit and had then told me that he considered this boy to be one of his most talented students, one from whom I could learn a great deal. His name was Wolfgang Pauli, and for the rest of his life he was to be a good friend, though often a very severe critic.

During years of studies under Arnold Sommerfeld, Max Born and Niels Bohr, Heisenberg and Pauli discussed problems of atomic theory, including especially the anomalous Zeeman effects and the helium energy states. After Pauli left Munich in fall 1921 for Göttingen, Copenhagen and then Hamburg, the friends began an intensive correspondence that continued, nearly without interruption, until Pauli’s death in 1958. Many of their letters have been preserved; they allow the reconstruction in some detail of their scientific collaboration over 37 years. It is one of the most active and fruitful collaborations in the whole history of science, whose early part contributed essentially to the first formulation of a consistent quantum mechanics in summer 1925 and, less than two years later, to its physical interpretation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    W. Heisenberg: Physics and Beyond (Harper and Row, New York, Evanston, London 1971) p. 24Google Scholar
  2. [2]
    The quote from Pauli’s letter to Jordan is from Scientific Correspondence I, p. 386. Jordan indeed was the first person ever to deal with quantum field theoretical problems in quantum mechanics. (See M. Born, W. Heisenberg, P. Jordan: Zur Quantenmechanik. II. Z. Phys. 35, 557–615 (1926); esp. Chapter 4.3; reprinted in Collected Works AI, pp. 399–455, esp. p. 446–455.) Usually, the paper of P.A.M. Dirac on the quantum theory of radiation is quoted as the pioneering paper on quantum field theory: The quantum theory of the emission and absorption of radiation. Proc. Roy. Soc. (London) A114, 243–265 (1927). Both Jordan and Dirac remained most active contributors to the first phase of quantum field theory. See, e.g., J. Schwinger, ed.: Selected Papers on Quantum Electrodynamics (Dover, New York 1958).CrossRefzbMATHGoogle Scholar
  3. [3]
    Pauli to Wentzel, 16 May 1927 (Scientific Correspondence I. p. 393)Google Scholar
  4. [4]
    P. Jordan, W. Pauli: Zur Quantenelektrodynamik ladungsfreier Felder. Z. Phys. 47, 151–173 (1928)CrossRefzbMATHGoogle Scholar
  5. [5]
    C.G. Darwin to W. Pauli, 11 January 1928 (Scientific Correspondence I, p. 424). Dirac’s paper was submitted on 2 January 1928: The quantum theory of the electron. Proc. Roy. Soc. (London) A117, 610–627 (1928).Google Scholar
  6. [6]
    See G. Breit to P. Ehrenfest, 30 November 1928 (quoted in Scientific Correspondence I, p. 478) and Breit’s later publication: The effect of retardation on the interaction of two electrons. Phys. Rev. (2) 34, 553–573 (1929).CrossRefGoogle Scholar
  7. [7]
    W. Pauli to O. Klein, 18 February 1929 (Scientific Correspondence I, p. 488–489). Oskar Klein also contributed to the early quantum field theory — see his paper with P. Jordan: Zum Mehrkörperproblem der Quantentheorie. Z. Phys. 45, 751–765 (1927).CrossRefGoogle Scholar
  8. [8]
    W. Heisenberg, W. Pauli: Zur Quantendynamik der Wellenfelder. Z. Phys. 56, 1–61 (1929);CrossRefzbMATHGoogle Scholar
  9. [8a]
    Zur Quantentheorie der Wellenfelder. II. Z. Phys. 59, 168–190 (1930). These papers were reprinted in Collected Works AII, pp. 8–68, 69–91. See also the annotation by R. Haag, ibid., pp. 3–7.CrossRefGoogle Scholar
  10. [9]
    J.R. Oppenheimer: Note on the theory of interaction of field and matter. Phys. Rev. (2) 35, 461–477 (1930)CrossRefzbMATHGoogle Scholar
  11. [10]
    For a general report on the development of this topic see the annotation of A. Pais in Collected Works AII, pp. 95–105.Google Scholar
  12. [11]
    L. Landau, R. Peierls: Quantenelektrodynamik im Konfigurationsraum. Z. Phys. 62, 188–200 (1930);CrossRefGoogle Scholar
  13. [11a]
    Erweiterung des Unbestimmheitsprinzips für die relativistische Quantenfeldtheorie. Z. Phys. 69, 56–69 (1931)CrossRefGoogle Scholar
  14. [12]
    N. Bohr, L. Rosenfeld: Zur Frage der Meßbarkeit der elektromagnetischen Größen. Danske Videnskab. Selskab, Math.-fys. Medd. 12, No. 8 (1933).Google Scholar
  15. [12a]
    For a historical discussion of the problem see L.M. Brown, H. Rechenberg: Landau’s work on quantum field theory and high energy physics (1930–61). In Frontiers of Physics (Proc. Landau Memorial Conf. 1988), ed. by E. Gotsman, Y. Ne’eman, A. Voronel (Pergamon, Oxford, etc. 1990) pp. 53–81.Google Scholar
  16. [13]
    W. Pauli, V.F. Weisskopf: Über die Quantisierung der skalaren relativistischen Wellengleichung. Helv. Phys. Acta 7, 709–731 (1934)Google Scholar
  17. [14]
    W. Heisenberg: Bemerkungen zur Diracschen Theorie des Positrons. Z. Phys. 90, 209–231 (1934);CrossRefGoogle Scholar
  18. [14a]
  19. [14b]
    Über die mit der Entstehung von Materie aus Strahlung verknüpften Ladungsschwankungen. Ber. Sächs. Akad. Wiss. (Leipzig), Math.-phys. Kl. 86, 317–322 (1934) — reprinted in Collected Works AII, pp. 132–154, 161; 155–160;Google Scholar
  20. [14c]
    W. Heisenberg, H. Euler: Folgerungen aus der Diracschen Theorie des Positrons. Z. Phys. 98, 714–732 (1936); reprinted in Collected Works AII, pp. 162–180.CrossRefGoogle Scholar
  21. [14d]
    See also H. Euler, B. Kockel: Über die Streuung von Licht nach der Diracschen Theorie. Die Naturwissenschaften 23, 246–247 (1935); V.F. Weisskopf: Über die Elektrodynamik des Vakuums aufgrund der Quantentheorie des Elektrons. Kgl. Danske Videnskab. Selskab, Math.-fys. Medd. 14, No. 6 (1936).CrossRefGoogle Scholar
  22. [15]
    V.F. Weisskopf: Über die Selbstenergie des Elektrons. Z. Phys. 89, 27–39 (1934);CrossRefGoogle Scholar
  23. [15a]
    Berichtigung zu der Arbeit: Über die Selbstenergie des Elektrons. Z. Phys. 90, 817–818 (1934)CrossRefGoogle Scholar
  24. [16]
    Heisenberg to Pauli, 28 October 1934 (Scientific Correspondence II, p. 356). The previous quotation is from Heisenberg to Pauli, 16 June 1934 (Scientific Correspondence II, p. 333).Google Scholar
  25. [17]
    Heisenberg to Pauli, 22 March 1935 (Scientific Correspondence II, p. 383). Note that the idea expressed here is, to some extent, realized in current supersymmetry theories.Google Scholar
  26. [18]
    W. Heisenberg to N. Bohr, 18 September 1930 (Niels Bohr Archive, Copenhagen)Google Scholar
  27. [19]
    For a more detailed discussion of the problem of nuclear forces see the annotation of L. Brown and H. Rechenberg in Collected Works AII, pp. 188–196.Google Scholar
  28. [20]
    W. Pauli to W. Heisenberg, 1 November 1934 (Scientific Correspondence II, p. 357)Google Scholar
  29. [21]
    Heisenberg to Pauli, 23 May 1936 (Scientific Correspondence II, p. 443)Google Scholar
  30. [22]
    W. Heisenberg: Zur Theorie der “Schauer” in der Höhenstrahlung. Z. Phys. 101, 533–540 (1936); reprinted in Collected Works AII, pp. 275–282Google Scholar
  31. [23]
    See the Heisenberg-Pauli correspondence of fall 1936 (Scientific Correspondence II, pp. 451–493).Google Scholar
  32. [24]
    Heisenberg to Pauli, 18 December 1936 (Scientific Correspondence II, p. 491)Google Scholar
  33. [25]
    L. de Broglie: Sur la nature du photon. Comptes Rendus (Paris) 198, 135–137 (1934)Google Scholar
  34. [26]
    G. Wentzel: Zur Frage der Äquivalenz von Lichtquanten und Korpuskelpaaren. Z. Phys. 92, 337–358 (1934);CrossRefGoogle Scholar
  35. [26a]
    P. Jordan: Zur Neutrinotheorie des Lichtes Z. Phys. 93, 464–472 (1935);CrossRefGoogle Scholar
  36. [26b]
    Beiträge zur Neutrinotheorie des Lichtes. I, II. Z. Phys. 102, 243–252 (1936), 105, 114–121 (1937);CrossRefGoogle Scholar
  37. [26c]
    105, 114–121 (1937);CrossRefGoogle Scholar
  38. [26d]
    R. de L. Kronig: Zur Neutrinotheorie des Lichtes. Physica 2, 491–498, (1935);CrossRefGoogle Scholar
  39. [26e]
  40. [26f]
  41. [26g]
    The neutrino theory of radiation and the emission of β-rays. Nature 137, 149 (1936).CrossRefzbMATHGoogle Scholar
  42. [26h]
    For a review of the topic see L. Brown, H. Rechenberg: Quantum field theories, nuclear forces, and cosmic rays. Am. J. Phys. 59, 595–605 (1991); esp. Section III.CrossRefGoogle Scholar
  43. [27]
    E.C.G. Stückelberg: Austauschkräfte zwischen Elementarteilchen und Fermi’sehe Theorie des β-Zerfalls als Konsequenzen einer möglichen Feldtheorie der Materie. Helv. Phys. Acta 9, 389–404 (1936);Google Scholar
  44. [27a]
    Die Wechselwirkungskräfte in der Elektrodynamik und der Feldtheorie der Kernkräfte. I, II. Helv. Phys. Acta 11, 225–244, (1938)zbMATHGoogle Scholar
  45. [27b]
  46. [28]
    See especially the Pauli correspondence in January and February 1934 (Scientific Correspondence II, pp. 265–283). Pauli also followed the later development with critical interest (see Scientific Correspondence II, 1934–1936).Google Scholar
  47. [29]
    See his letters to Heisenberg, January-May 1937 (Scientific Correspondence II, pp. 500–521).Google Scholar
  48. [30]
    S.H. Neddermeyer, C.D. Anderson: Note on the nature of cosmic ray particles. Phys. Rev. (2) 51, 884–886 (1937);CrossRefGoogle Scholar
  49. [30a]
    J.C. Street, E.C. Stevenson: Penetrating corpuscular component of the cosmic radiation. Phys. Rev. (2) 51, 1005 (1937);Google Scholar
  50. [30b]
    Y. Nishina, M. Takeuchi, T. Ichimiya: On the nature of cosmic ray particles. Phys. Rev. (2) 52, 1198–1199 (1937).CrossRefGoogle Scholar
  51. [30c]
    On the influence of the discovery of the mesotron on the “high-energy” physicists see H. Rechenberg and L.M. Brown: Yukawa’s heavy quantum and the mesotron (1935–1937). Centaurus 33, 214–252 (1990);CrossRefGoogle Scholar
  52. [30d]
    P. Galison: The discovery of the muon and the failed revolution against quantum electrodynamics. Centaurus 26, 262–316 (1983).CrossRefMathSciNetGoogle Scholar
  53. [31]
    Heisenberg to Pauli, 12 June 1937 (Scientific Correspondence II, p. 523)Google Scholar
  54. [32]
    H. Yukawa: On the interaction of elementary particles. I. Proc. Phys.-Math. Soc. Japan 17, 48–57 (1935)Google Scholar
  55. [33]
    H. Yukawa, S. Sakata, M. Taketani: On the interaction of elementary particles. III. Proc. Phys.-Math. Soc. Japan 20, 319–340 (1938);zbMATHGoogle Scholar
  56. [33a]
    H. Yukawa, S. Sakata, M. Kobayashi, M. Taketani: On the interaction of elementary particles. IV. Proc. Phys.-Math. Soc. Japan 20, 720–745 (1938);zbMATHGoogle Scholar
  57. [33b]
    H. Fröhlich, W. Heitier, N. Kemmer: On the nuclear forces and and the magnetic moment of the neutron and the proton. Proc. Roy. Soc. (London) A166, 154–171 (1938);CrossRefGoogle Scholar
  58. [33c]
    N. Kemmer: Quantum theory of Einstein-Bose particles and nuclear interaction. Proc. Roy. Soc. (London) A166, 127–153;Google Scholar
  59. [33d]
    H.J. Bhabha: On the theory of heavy electrons and nuclear forces. Proc. Roy. Soc. (London) A166, 501–527 (1938).CrossRefGoogle Scholar
  60. [33e]
    A review of the meson theory in early 1938 has been given by L.M. Brown and H. Rechenberg: The development of the vector meson theory in Japan and Britain (1937–1938). Brit. J. Hist. Sci. 24, 405–433 (1991).CrossRefMathSciNetGoogle Scholar
  61. [34]
    W. Pauli: Théorie quantique relativiste des particules obéissant à la statistique de Einstein-Bose. Ann. Inst. H. Poincaré 6, 137–152 (1936)MathSciNetGoogle Scholar
  62. [35]
    M Fierz: Über die relativistische Theorie kräftefreier Teilchen mit beliebigem Spin. Helv. Phys. Acta 12, 3–37 (1939);CrossRefGoogle Scholar
  63. [35a]
    W. Pauli, M. Fierz: Über relativistische Feldgleichungen von Teilchen mit beliebigem Spin im elektromagnetischen Feld. Helv. Phys. Acta 12, 297–300 (1939);zbMATHGoogle Scholar
  64. [35b]
    On relativistic wave equations for particles of arbitrary spin in an electromagnetic field. Proc. Roy. Soc. (London) A173, 211–232 (1939).MathSciNetGoogle Scholar
  65. [35b]
    See also the paper W. Pauli, F.J. Belinfante: On the statistical behaviour of known and unknown elementary particles. Physica 7, 177–192 (1940).CrossRefMathSciNetGoogle Scholar
  66. [36]
    A review of the cosmic ray work of Heisenberg has been given by E. Bagge in his annotation to Group 8 (Collected Works AII, pp. 241–249).Google Scholar
  67. [37]
    W. Heisenberg: Die Grenzen der Anwendbarkeit der bisherigen Quantentheorie. Z. Phys. 110, 251–266 (1938), esp. p. 265; reprinted in Collected Works AII, pp. 315–330CrossRefGoogle Scholar
  68. [38]
    W. Heisenberg: Zur Theorie der explosiven Schauer in der kosmischen Strahlung. II. Z. Phys. 113, 61–86 (1939); reprinted in Collected Works AII, pp. 337–362CrossRefzbMATHGoogle Scholar
  69. [39]
    Heisenberg to Pauli, 23 April 1939 (Scientific Correspondence II, pp. 634–635)Google Scholar
  70. [40]
    Pauli to Heisenberg, 10 June 1939 (Scientific Correspondence II, p. 664)Google Scholar
  71. [41]
    Pauli later published extended versions of his part of the Solvay report in two papers: The connection between spin and statistics. Phys. Rev. (2) 58, 716–722 (1940); Relativistic field theories of elementary particles. Rev. Mod. Phys. 13, 203–232 (1941).Google Scholar
  72. [41a]
    Heisenberg’s part would be reproduced from the manuscript only 45 years after the submission: Bericht über die allgemeinen Eigenschaften der Elementarteilchen. In Collected Works B, pp. 346–358Google Scholar
  73. [42]
    See the annotation of K. Wirtz to Group 9 of Heisenberg’s papers in Collected Works AII, pp. 365–370.Google Scholar
  74. [43]
    W. Pauli, S.M. Dancoff: The pseudoscalar meson field with strong coupling. Phys. Rev. (2) 62, 85–108 (1942);CrossRefzbMATHMathSciNetGoogle Scholar
  75. [43a]
    W. Pauli, S. Kusaka: On the theory of a mixed pseudoscalar and a vector field. Phys. Rev. (2) 63, 400–416 (1943);CrossRefzbMATHMathSciNetGoogle Scholar
  76. [43b]
    W. Pauli: On applications of the λ-limiting process to the theory of the meson field. Phys. Rev. (2) 64, 332–344 (1943);CrossRefzbMATHMathSciNetGoogle Scholar
  77. [43c]
    W. Pauli, N. Hu: On the strong coupling case for spin-dependent interaction in scalar- and vector-pair theories. Rev. Mod. Phys. 17, 267–286 (1945)CrossRefzbMATHMathSciNetGoogle Scholar
  78. [44]
    W. Pauli: Meson Theory of Nuclear Forces (Interscience, New York, London 1946; 2nd edition 1948)zbMATHGoogle Scholar
  79. [45]
    P.A.M. Dirac: The physical interpretation of quantum mechanics. Proc. Roy. Soc. (London) A180, 1–40 (1942)CrossRefMathSciNetGoogle Scholar
  80. [46]
    W. Pauli: On Dirac’s new method of field quantization. Rev. Mod. Phys. 15, 175–207 (1943);CrossRefzbMATHMathSciNetGoogle Scholar
  81. [46a]
    W. Pauli, J.M. Jauch: On the application of Dirac’s method of field quantization to the problem of emission of low energy photons. Phys. Rev. (2) 65, 255–256 (1944);Google Scholar
  82. [46b]
    W. Pauli: Dirac’s Feldquantisierung und Emission von Photonen kleiner Frequenz. Helv. Phys. Acta 19, 234–237 (1946)Google Scholar
  83. [47]
    He especially organized at the Kaiser Wilhelm-Institut für Physik seminars on cosmic ray physics, which analyzed and summarized the recent data and theories. These review talks were collected in a book, Kosmische Strahlung (Springer, Berlin 1943), edited by W. Heisenberg. He himself contributed five articles, reprinted in Collected Works B, pp. 365–406.Google Scholar
  84. [48]
    See the papers to Group 10 and the annotation of R. Oehme in Collected Works AII, pp. 605–713.Google Scholar
  85. [49]
    The origin and development of S-matrix theory has been discussed by H. Rechenberg: The early S-matrix theory and its propagation (1942–1952). In Pions to Quarks, ed. by L.M. Brown, M. Dresden, L. Hoddeson (Cambridge University Press, Cambridge 1989) pp. 551-578.CrossRefGoogle Scholar
  86. [50]
    See especially the review article of W. Heisenberg: Der mathematische Rahmen der Quantentheorie der Wellenfelder.Z. Naturforsch. 1, 608–622 (1946); reprinted in Collected Works AII, pp. 699–713.zbMATHMathSciNetGoogle Scholar
  87. [51]
    W. Pauli: Difficulties of field theories and of field quantization. In Report of an International Conference on Fundamental Particles and Low Temperatures, Cambridge 1946. Vol. I: Fundamental Particles (The Physical Society, London 1947) pp. 5–9, esp. p. 6Google Scholar
  88. [52]
    Pauli to Heisenberg, 9 September 1946 (Werner-Heisenberg-Archiv)Google Scholar
  89. [53]
    S.T. Ma: Redundant zeros in the discrete energy spectra of Heisenberg’s theory of the characteristic matrix. Phys. Rev. (2) 69, 668 (1946)CrossRefGoogle Scholar
  90. [54]
    R. Jost to W. Heisenberg, 27 January 1947 (Werner-Heisenberg-Archiv); R. Jost: Über die falschen Nullstellen der Energieweite der S-Matrix. Helv. Phys. Acta 20, 256–266 (1947). Actually Pauli was quite mistaken in attacking the use of analyticity in S-matrix theory; thus, Ma’s unphysical poles later found a satisfactory physical interpretation (see R. Oehme’s annotation to the S-matrix papers in Collected Works AII, esp. p. 607).MathSciNetGoogle Scholar
  91. [55]
    Pauli to Heisenberg, 25 December 1946 (Werner-Heisenberg-Archiv). This and the following letters will be published in Scientific Correspondence III. Google Scholar
  92. [56]
    Heisenberg to Pauli, 29 April 1948 (Werner-Heisenberg-Archiv)Google Scholar
  93. [57]
    Pauli to Heisenberg, 22 January 1948 (Werner-Heisenberg-Archiv)Google Scholar
  94. [58]
    Pauli to Heisenberg, 4 May 1948 (Werner-Heisenberg-Archiv)Google Scholar
  95. [59]
    Pauli to Heisenberg, 20 October 1948 (Werner-Heisenberg-Archiv)Google Scholar
  96. [60]
    W. Pauli, F. Villars: On the invariant regularisation in relativistic quantum theory. Rev. Mod. Phys. 21, 434–444 (1949)CrossRefzbMATHMathSciNetGoogle Scholar
  97. [61]
    See, e.g., the handbook article of G. Källén: Quantenelektrodynamik. In Handbuch der Physik. Vol. V/1, ed. by S. Flügge (Springer, Berlin, Göttingen, Heidelberg 1958) pp. 168–364.Google Scholar
  98. [62]
    W. Pauli: Etat actuel de la théorie quantique des champs. La renormalization. In Particules Fondamentales et Noyaux, Paris 1950 (Colloq. Intern. Centre Nat. Rech. Sci., Paris) 38, 67–77 (1953); esp. p. 72Google Scholar
  99. [63]
    W. Pauli: On the Hamiltonian structure of non-local field theories. Il Nuovo Cimento 10, 648–667 (1953)CrossRefzbMATHMathSciNetGoogle Scholar
  100. [64]
    W. Heisenberg, ed.: Kosmische Strahlung (Springer, Berlin, Göttingen, Heidelberg 1953)zbMATHGoogle Scholar
  101. [65]
    See the papers presented in Group 11 of this volume and the annotation of H. Koppe, and the second part of the papers collected in Group 1 and annotated by S. Chandrasekhar in Collected Works AII.Google Scholar
  102. [66]
    See the papers presented in Group 12 of this volume and the annotation by R. Hagedorn.Google Scholar
  103. [67]
    G. Källén, W. Pauli: On the mathematical structure of T.D. Lee’s model of a renormalizable field theory. Kgl. Danske Videnskab. Selskab, Math.-Fys. Medd. 30, No. 7 (1955)Google Scholar
  104. [68]
    W. Heisenberg: Physics and Beyond, Ref. 1, p. 233Google Scholar
  105. [69]
    W. Heisenberg, Ref. 1, p. 234Google Scholar
  106. [70]
    W. Heisenberg, Ref. 1, p. 234–235Google Scholar
  107. [71]
    W. Heisenberg, Ref. 1, pp. 235–236Google Scholar
  108. [72]
    W. Heisenberg, Ref. 1, p. 236Google Scholar
  109. [73]
    D. Cassidy: Cosmic ray showers, high energy physics, and quantum field theories: Programmatic interactions in the 1930s. Hist. Stud. Phys. Sci. 12, 1–39 (1981)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Helmut Rechenberg

There are no affiliations available

Personalised recommendations