Advertisement

The Spin pp 1-60 | Cite as

Spin, or actually: Spin and Quantum Statistics

  • Jürg Fröhlich
Part of the Progress in Mathematical Physics book series (PMP, volume 55)

Abstract

The history of the discovery of electron spin and the Pauli principle and the mathematics of spin and quantum statistics are reviewed. Pauli’s theory of the spinning electron and some of its many applications in mathematics and physics are considered in more detail. The role of the fact that the tree-level gyromagnetic factor of the electron has the value g e = 2 in an analysis of stability (and instability) of matter in arbitrary external magnetic fields is highlighted. Radiative corrections and precision measurements of g e are reviewed. The general connection between spin and statistics, the CPT theorem and the theory of braid statistics, relevant in the theory of the quantum Hall effect, are described.

“He who is deficient in the art of selection may, by showing nothing but the truth, produce all the effects of the grossest falsehoods. It perpetually happens that one writer tells less truth than another, merely because he tells more ‘truth’.” (T. Macauley, ‘History’, in Essays, Vol. 1, p 387, Sheldon, NY 1860)

Keywords

Unitary Representation Pauli Principle Superselection Sector Thomas Precession Zeeman Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Pais, Inward Bound, Oxford University Press, New York, 1986.Google Scholar
  2. [2]
    H. Kragh, Quantum Generations, Princeton University Press, Princeton, 1999.MATHGoogle Scholar
  3. [5]
    J. Fröhlich, Réflexions sur Wolfgang Pauli, proceedings of the “Colloque 2000: Pensée et Science” of the Fondation F. Gonseth, Eric Emery (ed.), Rev. Synt. 126 (2005), 443–450.Google Scholar
  4. [6]
    N. Straumann, Quantenmechanik, Springer-Verlag, 2002.Google Scholar
  5. [7]
    W. Pauli, Z. Physik 16 (1923), 155–164.CrossRefADSGoogle Scholar
  6. [8]
    W. Pauli, Z. Physik 31 (1925), 373–385.CrossRefADSGoogle Scholar
  7. [9]
    S. Ferrara, M. Porrati, V.L. Telegdi, Phys. Rev. D 46 (1992), 3529–3537.CrossRefADSGoogle Scholar
  8. [10]
    J.D. Jackson, Classical Eletromagnetism, John Wiley&Sons, New York, 1975.Google Scholar
  9. [11]
    W. Pauli, Z. Physik 31 (1925), 765–783.CrossRefADSGoogle Scholar
  10. [12]
    E.C. Stoner, Phil. Magazine 48 (1924), 719–736.Google Scholar
  11. [13]
    W. Heisenberg, Zeitschrift für Physik 33 (1925), 879–893.CrossRefADSGoogle Scholar
  12. [14]
    M. Born, P. Jordan, Zeitschrift für Physik 34 (1925), 858–888.CrossRefADSGoogle Scholar
  13. [15]
    M. Born, W. Heisenberg, P. Jordan, Zeitschrift für Physik 35 (1926), 557–615.CrossRefADSGoogle Scholar
  14. [16]
    P.A.M. Dirac, Proc. Royal Soc. (London) A 109 (1925), 642–653.CrossRefADSGoogle Scholar
  15. [17]
    E. Schrödinger, Annalen der Physik 79 (1926), 361–376; Annalen der Physik 76 (1926), 146-147; Annalen der Physik 80 (1926), 437-490.CrossRefGoogle Scholar
  16. [18]
    P.A.M. Dirac, Proc. Royal Soc. A 117 (1928), 610; A 118 (1928), 351.CrossRefADSGoogle Scholar
  17. [19]
    W. Pauli, Z. Physik 43 (1927), 601–623.CrossRefADSGoogle Scholar
  18. [20]
    J. Fröhlich, O. Grandjean, A. Recknagel, Comm. Math. Phys. 193 (1998), 527–594.MATHCrossRefADSMathSciNetGoogle Scholar
  19. [21]
    J. Fröhlich, The Electron is Inexhaustible, Amer. Math. Soc. Publ., Providence RI, 1999.Google Scholar
  20. [22]
    D. Salamon, Spin Geometry and Seiberg-Witten Invariants, preprint 1995.Google Scholar
  21. [23]
    A. Connes, Noncommutative Geometry, Academic Press, New York 1994.MATHGoogle Scholar
  22. [24]
    J. Fuchs, Chr. Schweigert, Symmetries, Lie Algebras and Representations, Cambridge University Press, Cambridge, New York 1997.MATHGoogle Scholar
  23. [25]
    G. Velo, D. Zwanziger, Phys. Rev. 186 (1969), 1337–1341; Phys. Rev. 188 (1969), 2218-2222; A.Z. Capri, R.L. Kobes, Phys. Rev. D 22 (1980), 1967-1978.CrossRefADSGoogle Scholar
  24. [26]
    S. Deser, B. Zumino, Phys. Lett. B 62 (1976), 335; K. Vonlanthen, Supergravitation und Velo-Zwanziger Phänomene, ETH diploma thesis 1978 (N. Straumann, advisor).CrossRefADSMathSciNetGoogle Scholar
  25. [27]
    J. Fröhlich, U.M. Studer, E. Thiran, Quantum Theory of Large Systems of Non-Relativistic Matter, in: Fluctuating Geometries in Statistical Mechanics and Field Theory, Les Houches, Session LXII (1994), F. David, P. Ginsparg, J. Zinn-Justin (eds.), Elsevier, New York, 1996.Google Scholar
  26. [28]
    R. Howe, Lect. Appl. Math. 21 (1985), 179.MathSciNetGoogle Scholar
  27. [29]
    S. Weinberg, The Quantum Theory of Fields, Vol. 1, Cambridge University Press, Cambridge, New York, 1995; J. Fröhlich, Einführung in die Quantenfeldtheorie, ETH Lecture Notes, 1986.Google Scholar
  28. [30]
    W. Hunziker, Commun. Math. Phys. 40 (1975), 215–222.CrossRefMathSciNetADSGoogle Scholar
  29. [31]
    E.H. Lieb, The Stability of Matter: From Atoms to Stars, 4th edition, Springer-Verlag, 2005.Google Scholar
  30. [32]
    J. Fröhlich, E.H. Lieb, M. Loss, Commun. Math. Phys. 104 (1986), 251–270.MATHCrossRefADSGoogle Scholar
  31. [33]
    M. Loss, H.-T. Yau, Commun. Math. Phys. 104 (1986), 283–290.MATHCrossRefADSMathSciNetGoogle Scholar
  32. [34]
    E.H. Lieb, M. Loss, Commun. Math. Phys. 104 (1986), 271–282.MATHCrossRefADSMathSciNetGoogle Scholar
  33. [35]
    C. Fefferman, Proc. Natl. Acad. Science USA 92 (1985), 5006–5007, and Lecture Notes.CrossRefADSMathSciNetGoogle Scholar
  34. [36]
    E.H. Lieb, M. Loss, J.-Ph. Solovej, Phys. Rev. Letters 75 (1995), 985–989.MATHCrossRefADSMathSciNetGoogle Scholar
  35. [37]
    J. Fröhlich, Ann. Inst. H. Poincaré 19 (1974), 1–103; Fortschritte der Physik 22 (1974), 159-198.Google Scholar
  36. [38]
    L. Bugliaro Goggia, J. Fröhlich, G.M. Graf, Phys. Rev. Letters 77 (1996), 3494–3497.CrossRefADSGoogle Scholar
  37. [39]
    C. Fefferman, J. Fröhlich, G.M. Graf, Proc. Natl. Acad. Sci. 93 (1996), 15009–15011.CrossRefADSGoogle Scholar
  38. [40]
    C. Fefferman, J. Fröhlich, G.M. Graf, Commun. Math. Phys. 190 (1999), 309–330.CrossRefADSGoogle Scholar
  39. [41]
    L. Bugliaro Goggia, C. Fefferman, J. Fröhlich, G.M. Graf, J. Stubbe, Commun. Math. Phys. 187 (1997), 567–582.CrossRefADSGoogle Scholar
  40. [42]
    L. Bugliaro Goggia, C. Fefferman, G.M. Graf, Revista Matematica Iberoamericana 15 (1999), 593–619.MathSciNetGoogle Scholar
  41. [43]
    V. Bach, J. Fröhlich, I.M. Sigal, Adv. Math. 137 (1998), 205–298; 137 (1998), 299-395.MATHCrossRefMathSciNetGoogle Scholar
  42. [44]
    V. Bach, J. Fröhlich, I.M. Sigal, Commun. Math. Phys. 207 (1999), 249–290.MATHCrossRefADSGoogle Scholar
  43. [45]
    M. Griesemer, M. Loss, E.H. Lieb, Inventiones Math. 145 (1999), 557–587.CrossRefMathSciNetADSGoogle Scholar
  44. [46]
    J. Fröhlich, M. Griesemer, B. Schlein, Adv. Math. 164 (2001), 349–398.MATHCrossRefMathSciNetGoogle Scholar
  45. [47]
    J. Fröhlich, M. Griesemer, B. Schlein, Ann. Henri Poincaré 3 (2002), 107–170.MATHCrossRefGoogle Scholar
  46. [48]
    V. Bach, J. Fröhlich, A. Pizzo, Comm. Math. Phys. 264 (2006), 145–165; Comm. Math. Phys. 274 (2007), 457-486; Adv. Math. (to appear).MATHCrossRefADSMathSciNetGoogle Scholar
  47. [49]
    T. Chen, J. Fröhlich, A. Pizzo, Infraparticle Scattering States in Non-Relativistic QED: I & II, preprints 2007.Google Scholar
  48. [50]
    H. Spohn, Dynamics of Charged Particles and Their Radiation Field, Cambridge University Press, Cambridge, New York, 2004.MATHCrossRefGoogle Scholar
  49. [51]
    T. Chen, ETH Diploma Thesis, 1994.Google Scholar
  50. [54]
    M. Fierz, Helv. Phys. Acta 12 (1939), 3.CrossRefGoogle Scholar
  51. [55]
    R. Jost, The General Theory of Quantized Fields, AMS Publ., Providence RI, 1965.MATHGoogle Scholar
  52. [56]
    R.F. Streater, A.S. Wightman, PCT, Spin and Statistics and All That, Benjamin, New York, 1964.MATHGoogle Scholar
  53. [57]
    J. Glimm, A. Jaffe, Quantum Physics: A functional Integral Point of View, Springer-Verlag, 1987.Google Scholar
  54. [58]
    S. Doplicher, R. Haag, J.E. Roberts, Commun. Math. Phys. 33 (1971), 199; Commun. Math. Phys. 35 (1974), 49.CrossRefADSMathSciNetGoogle Scholar
  55. [59]
    S. Doplicher, J.E. Roberts, Commun. Math. Phys. 131 (1990), 51.MATHCrossRefADSMathSciNetGoogle Scholar
  56. [60]
    G. Lüdrs, Kong. Dansk. Vid. Selskab, Mat.-Fys. Medd. 28 (1954), 5; Ann. Phys. 2 (1957), 1; W. Pauli, Nuovo Cimento 6 (1957), 204.Google Scholar
  57. [61]
    R. Jost, Helv. Phys. Acta 30 (1957), 409.MATHMathSciNetGoogle Scholar
  58. [62]
    R. Kubo, J. Phys. Soc. Japan 12 (1957), 57; P.C. Martin, J. Schwinger, Phys. Rev. 115 (1959), 1342; R. Haag, N. Hugenholtz, M. Winnink, Commun. Math. Phys. 5 (1967), 215.Google Scholar
  59. [63]
    J.J. Bisognano, E.H. Wichmann, J. Math. Phys. 16 (1975), 985–1007.MATHCrossRefMathSciNetADSGoogle Scholar
  60. [64]
    M. Takesaki, Tomita’s Theory of Modular Hilbert Algebras and its Applications, Lecture Notes in Mathematics 128, Springer-Verlag, 1970; O. Bratteli, D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Springer-Verlag, 1979, 1981.Google Scholar
  61. [65]
    R.F. Streater, I.F. Wilde, Nucl. Phys. B 24 (1970), 561.CrossRefADSGoogle Scholar
  62. [66]
    J. Fröhlich, Commun. Math. Phys. 47 (1976), 269–310.CrossRefADSGoogle Scholar
  63. [67]
    M. Leinaas, J. Myrheim, Il Nuovo Cimento 37B (1977), 1.Google Scholar
  64. [68]
    G.A. Goldin, R. Menikoff, D.H. Sharp, J. Math. Phys. 22 (1981), 1664.CrossRefADSMathSciNetGoogle Scholar
  65. [69]
    F. Wilczeck, Phys. Rev. Letters 48 (1982), 1144; 49 (1982), 957.CrossRefADSGoogle Scholar
  66. [70]
    J. Fröhlich, P.A. Marchetti, Lett. Math. Phys. 16 (1988), 347; Commun. Math. Phys. 121 (1988), 177.MATHCrossRefADSMathSciNetGoogle Scholar
  67. [71]
    J. Fröhlich, Statistics of Fields, the Yang-Baxter Equation and the Theory of Knots and Links, in: Non-Perturbative Quantum Field Theory, Cargèse 1987, G. ’t Hooft et al. (eds.), Plenum Press, New York, 1988. J. Fröhlich, Statistics and Monodromy in Two-and Three-Dimensional Quantum Field Theory, in: Differential Geometrical Methods in Theoretical Physics, K. Bleuler, M. Werner (eds.), Kluwer Academic Publ., Dordrecht, 1988.Google Scholar
  68. [72]
    K. Fredenhagen, K.H. Rehren, B. Schroer, Commun. Math. Phys. 125 (1989), 201.MATHCrossRefADSMathSciNetGoogle Scholar
  69. [73]
    J. Fröhlich, F. Gabbiani, Rev. Math. Phys. 2 (1990), 251; J. Fröhlich, P.A. Marchetti, Nucl. Phys. B 356 (1991), 533.MATHCrossRefMathSciNetGoogle Scholar
  70. [74]
    L. Birke, J. Fröhlich, Rev. Math. Phys. 14 (2002), 829.MATHCrossRefMathSciNetGoogle Scholar
  71. [75]
    S. Weinberg, E. Witten, Phys. Letters B 96 (1980), 59.CrossRefADSMathSciNetGoogle Scholar
  72. [76]
    D. Buchholz, K. Fredenhagen, Commun. Math. Phys. 84 (1982), 1.MATHCrossRefADSMathSciNetGoogle Scholar
  73. [77]
    K. Osterwalder, R. Schrader, Commun. Math. Phys. 42 (1975), 281; see also V. Glaser, Commun. Math. Phys. 37 (1974), 257.MATHCrossRefMathSciNetADSGoogle Scholar
  74. [78]
    H. Araki, J. Math. Phys. 2 (1961), 267; W. Schneider, Helv. Phys. Acta 42 (1969), 201.MATHCrossRefADSMathSciNetGoogle Scholar
  75. [79]
    J. Fröhlich, T. Kerler, Quantum Groups, Quantum Categories and Quantum Field Theory, Lecture Notes in Mathematics, Vol. 1542, Springer-Verlag, 1993.Google Scholar
  76. [80]
    J. Fuchs, I. Runkel, Chr. Schweigert, Nucl. Phys. B 624 (2002), 452; Nucl. Phys. B 646 (2002), 353.MATHCrossRefADSMathSciNetGoogle Scholar
  77. [81]
    R.E. Prange, S.M. Girvin (eds.), The Quantum Hall Effect, Graduate Texts in Contemporary Physics, Springer-Verlag, 1990; M. Stone (ed.), Quantum Hall Effect, World Scientific Publ., Singapore, London, Hong Kong, 1992.Google Scholar
  78. [82]
    J. Fröhlich, The Fractional Quantum Hall Effect, Chern-Simons Theory, and Integral Lattices, in: Proc. of ICM’ 94, S.D. Chatterji (ed.), Birkhäuser Verlag, 1995. J. Fröhlich, B. Pedrini, Chr. Schweigert, J. Walcher, J. Stat. Phys. 103 (2001) 527; J. Fröhlich, B. Pedrini, in: Statistical Field Theory, Como 2001, A. Cappelli, G. Mussardo (eds.), Kluwer, New York, Amsterdam, 2002.Google Scholar
  79. [83]
    R. Jackiw, S. Templeton, Phys. Rev. D 23 (1981), 2291; S. Deser, R. Jackiw, S. Templeton, Phys. Rev. Letters 48 (1982), 975; R. Pisarski, S. Rao, Phys. Rev. D 32 (1985), 2081.CrossRefADSGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Jürg Fröhlich
    • 1
  1. 1.Theoretical PhysicsETH ZürichZürich

Personalised recommendations