In his Bakerian lecture in 1941 Dirac has suggested that in a relativistic quantum theory, use should be made of a state space with indefinite metric.1 This was a rather revolutionary suggestion, since in unrelativistic quantum theory the state space could always be interpreted as a Hilbert space with positive metric, and the whole probabilistic interpretation of the formalism of quantum theory rested upon this assumption. Dirac’s idea has been developed in the course of years in a great number of papers by many physicists, and it cannot be the intention of the present paper to give a more or less complete historical account of this development. Only its essential steps shall be briefly described and analysed, in order to arrive at conclusions about the significance of Dirac’s suggestion in the present relativistic theory of elementary particles. A few years ago a rather comprehensive survey of this whole field was given in a book by Nagy,2 which also quotes a large part of the related literature.


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  1. 1.
    P. A. M. Dirac, Proc. Roy. Soc. (London) A180, 1 (1942).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    K. L. Nagy, State Vector Spaces with Indefinite Metric in Quantum Field Theory ( Akademiai Kiadó, Budapest: 1966 ).zbMATHGoogle Scholar
  3. 3.
    W. Pauli, Rev. Mod. Phys. 15 (3), 175 (1943).MathSciNetADSCrossRefzbMATHGoogle Scholar
  4. 4.
    S. N. Gupta, Proc. Phys. Soc. (London) A LXIII, 681 (1950).Google Scholar
  5. 5.
    K. Bleuler, Hely. Phys. Acta XXIII, 567 (1950).Google Scholar
  6. 6.
    W. Heisenberg, Z. Naturforsch 9a, 292 (1954); Z. Physik 144, 1 (1956).MathSciNetADSCrossRefzbMATHGoogle Scholar
  7. 7.
    W. Heisenberg, Nucl. Phys. 4, 532 (1957).CrossRefzbMATHGoogle Scholar
  8. 8.
    W. Pauli and G. Källén, Math. Phys. Medd. 30, 7 (1955).Google Scholar
  9. 9.
    W. Pauli, Proceedings of the Annual International Conference on High-Energy Physics, CERN, p. 127 (Geneva: 1958 ).Google Scholar
  10. 10.
    E. C. G. Sudarshan, Phys. Rev. 123, 2183 (1961).MathSciNetADSCrossRefzbMATHGoogle Scholar
  11. 11.
    M. Karowski, Z. Naturforsch 24a, 510 (1969).ADSGoogle Scholar
  12. 12.
    H. P. Dürr and E. Rudolph, Nuovo Cimento X, 62A, 411 (1969).ADSCrossRefGoogle Scholar
  13. 13.
    H. P. Dürr and E. Rudolph, Nuovo Cimento X, 65A, 423 (1969).CrossRefGoogle Scholar
  14. 14.
    M. E. Arons, M. Y. Han and E. C. G. Sudarshan, Phys. Rev. 137, 4B, B1085 (1965).Google Scholar
  15. 15.
    T. D. Lee and G. C. Wick, Phys. Rev. D, 2, 6, 1033 (1970).MathSciNetADSCrossRefzbMATHGoogle Scholar
  16. 16.
    A. M. Gleeson, R. J. Moore, H. Rechenberg and E. C. G. Sudarshan, Analyticity, Covariance and Unitarity in Indefinite Metric Quantum Field Theories,CPT-77, AEC-26.Google Scholar
  17. 17.
    H. P. Dürr and E. Seiler, Nuovo Cimento X, 66A, 734 (1970).ADSCrossRefGoogle Scholar
  18. 18.
    W. Heisenberg, Introduction to the Unified Field Theory of Elementary Particles (J. Wiley and Sons, New York: 1966 ).Google Scholar

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© Springer-Verlag Berlin Heidelberg 1984

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  • W. Heisenberg

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