The Gauge Principle in Modern Physics

  • K. Bleuler
Part of the NATO ASI Series book series (NSSB, volume 144)


It is pointed out that the gauge principle which by now plays a decisive role in many domains of physics is based on a most natural mathematical, or, better geometrical view-point. In fact, all fundamental interactions known so far are due to this principle. It is stressed, in particular, that, according to our recent attempt, even nuclear physics may be directly incorporated into this general geometrical view-point.


Gauge Theory Nuclear Structure Colour Index Parallel Transport Spin Index 
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  1. 1.
    H. Weyl, Z. Physik, 56 (1929) 330ADSCrossRefGoogle Scholar
  2. 2.
    C.N. Yang, R. Mills, Phys. Rev., 95, 631, 96, 191 (1954)MathSciNetGoogle Scholar
  3. 2a.
    R. Utiyamah, Phys. Rev. 101 (1956) 1597MathSciNetADSCrossRefGoogle Scholar
  4. 3.
    M. Atiyah, The Math. Intelligencer, 6 (1984), 9MathSciNetGoogle Scholar
  5. 4.
    W. Drechsler, M.E. Mayer, Fibre Bundle Techniques in Gauge Theories, Springer Lect. Notes in Physics, 67 (1977)Google Scholar
  6. 4a.
    A. Trautman, Reports on Math. Phys. 1 (1970) 29MathSciNetADSzbMATHGoogle Scholar
  7. 4b.
    A. Held (ed.): General Relativity and Gravitation, Vol. 1, Plenum Press, New York (1980), 287Google Scholar
  8. 5.
    W. Heisenberg, Feldtheorie, Hirzel, Stuttgart (1967)Google Scholar
  9. 6.
    M. Gell’Mann, Y. Ne’eman, The Eightfold Way, W.A. Benjamin, New York (1964)Google Scholar
  10. 7.
    For example: C. Rebbi (ed.): Lattice Gauge Theories and Monte Carlo Simulations, World Scientific, Singapore (1983)Google Scholar
  11. 8.
    A new review can be found in: M. Diemoz et al., Nucleon Structure Functions from Neutrino Scattering, Physics Reports, 130 (1986) 5,6CrossRefGoogle Scholar
  12. 9.
    K. Bleuler et al., Z. Naturforschung 38a (1983) 705ADSGoogle Scholar
  13. 9a.
    K. Bleuler, Perpectives in Nuclear Physics, World Scientific, Singapore (1985) 455Google Scholar
  14. 9b.
    H.R. Petry, Lecture Notes in Physics, Vol. 197, Springer, Berlin (1983) 236Google Scholar
  15. 9c.
    H.R. Petry et al., Phys. Lett. 159B (1985) 363ADSGoogle Scholar
  16. 10.
    E.V. Shuryak, Nucl. Physics, B203 (1982) 93ADSGoogle Scholar
  17. 10a.
    E. Shuryak, The QCD Vacuum, Hadrons and Superdense Matter, World Scientific, Singapore (1986), to appearGoogle Scholar
  18. 11.
    G. t′Hooft, Phys. Rev., D14 (1976) 3432ADSGoogle Scholar
  19. 12.
    To be published in the Varenna Conference-report (1985), organized by Prof. E. Gadioli, Istituto di Fisiche dell Univ. di Milano, Via Celoria 16, I-20133 Milano, ItalienGoogle Scholar
  20. 13.
    J.L. Lopes, Gauge Field Theories, Pergamon Press (1983)Google Scholar
  21. 13a.
    Ch. Quigg, Gauge Theories of the Strong, Weak and Electromagnetic Interactions, Benjamin/Cummings (1983)Google Scholar
  22. 14.
    Y. Aharanov, D. Bohm, Phys. Rev. 115 (1959) 485MathSciNetADSCrossRefGoogle Scholar
  23. 15.
    H. Lipkin, Lie Groups for Pedestrians, North Holland (1967)Google Scholar
  24. 16.
    see, e.g. F.J. Yndurain, Quantum Chromodynamics, Springer 1983 (in particular, chap. I, Nr. 5)zbMATHGoogle Scholar
  25. 17.
    K. Bleuler, Helv.Phys.Acta XXIII (1956) 567: The main point herein: All state vectors in Hilbert space (endowed with indefinite metric) are only defined modulo the so-called ‘null-space’, i.e. a freedom which automatically generates (restricted) gauge transformations.MathSciNetGoogle Scholar
  26. 18.
    For a recent survey see e.g. Y. Ne’eman, Prog. Theoret. Phys. (Kyoto) Suppl. (to be published). From a gauge theoretical view-point strings represent an enormous enlargement of similar differential geometrical methods.Google Scholar
  27. 19.
    See e.g. ‘Differential Geometrical Methods in Mathematical Physics’ (edited by K. Bleuler and A. Reetz), Springer Lecture Notes in Mathematics, Nr. 570 (1975) At that time (see chapt. II), the advent of supersymmetry (in connection with graded manifolds) was enthusiastically wellcomed by mathematicians.Google Scholar
  28. 20.
    See e.g. “Group Theoretical Methods in Physics”, Springer Lecture Notes in Physics, Nr. 79, 94 a.s.o. and: “To fulfill a Vision”, Jerusalem Einstein Centennial Symposium, edited by Y. Ne’eman, Addison-Wesley (1981)Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • K. Bleuler
    • 1
  1. 1.Institut für Theoretische KernphysikUniversität BonnBonn 1West-Germany

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