Revival of the Old String Model

  • Yadin Y. Goldschmidt
Part of the Studies in the Natural Sciences book series (SNS, volume 19)


In this talk I would like to review the recent developments in the theory of strings induced by a novel approach due to Polyakov.1,2 The “old” string model3 of the early seventies had some severe problems that allowed a consistent treatment only when the space time dimensionality is 26. The important observation was that due to coordinate transformations invariance, also called “gauge” invariance, of the Nambu action, there are relations or constraints among the coordinates and momenta. In order to quantize the theory canonically, one can either eliminate redundant degrees of freedom and quantize noncovariantly or quantize covariantly and impose the constraints on the physical states. It turned out that in the first method, Lorentz covariance was recovered only in d=26, and in the second approach “ghost” states could be eliminated only at d = 26. In this space-time dimensionality both methods agree. But of course we are looking for a string theory which can be quantized in four dimensions.* Another problem of the “old” string model was the appearance of “tachyons” with imaginary mass.


Liouville Equation String Model Space Time Dimensionality Lorentz Covariance Redundant Degree 
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    A. M. Polyakov, Phys. Lett. 103B, 207 (1981).Google Scholar
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    A. M. Polyakov, Phys. Lett. 103B, 211 (1981).Google Scholar
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    For a review of the “old” string theory see S. Mandelstam, Phys. Rep. 13C, 261 (1974); C. Rebbi, Phys. Rep. 12C, 1 (1974); and “Dual Theory”, edited by M. Jacob, North Holland, and references therein.CrossRefGoogle Scholar
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    For a review of the trace anomaly and the proper time method see S. W. Hawking, Comm. Math. Phys. 55, 133 (1977) and V. N. Romanov and A. S. Schwarz, Theo. Mat. Fiz. 41, 190 (1979).CrossRefGoogle Scholar
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    Y. Y. Goldsehmidt, Physics Lett. B. - to be published. (Brown University preprint HET 463).Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • Yadin Y. Goldschmidt
    • 1
  1. 1.Brown UniversityProvidenceUSA

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