Abstract
This chapter describes the birth of string theory from the dual resonance models. It arose from the question of whether any dynamical models could underly them. Nambu, Susskind and Nielsen suggested a Rubber String Model as an answer. To aid understanding, the classical string and its action are revisited. The Nambu-Goto(NG) action is analysed in detail. First, a classical analysis is carried out, bringing out the constrained nature of this action. Important parallels with QED are brought out. In particular, the physical state construction in QED is explained in anticipation of similar issues with the NG-action. The equations of motion and the boundary conditions are also analysed. The conserved energy-momentum-currents arising out of Poincaré invariance in target space are worked out. The world-sheet reparametrization invariance is fixed by two coordinate conditions. The transversality of the physical d.o.f is also explained. The light-cone parametrization is presented in detail. Both covariant and non-covariant quantizations are discussed. The quantum Virasoro algebras and their differing central extensions in these two cases are analysed carefully. The physical state analysis and critical dimensions are further elaborated. The Arvis quantization of strings with fixed ends is also worked out. The chapter ends with a brief mention of path-integral quantization of strings.
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Notes
- 1.
The higher dimensional generalization of the non-relativistic string is somewhat unrealistic as it predicts equal velocities for transverse and longitudinal waves. A more realistic treatment of elastic media, as for example the one in Landau and Lifshitz book [13](see their Sect. 22), always yields \(c_l\,>\,\sqrt{\frac{4}{3}}\,c_t\).
References
H. Poincare, Science and Hypothesis (1902)
Y. Nambu, in Proceedings of International Conference on Symmetries and Quark Models, ed. by R. Chand (Wayne State University, Gordon and Breach, 1970)
Y. Nambu, Duality and Hadrodynamics. Lectures at the Copenhagen Symposium, 1970, reprinted in Broken Symmetry: Selected Papers of Y. Nambu, ed. by T. Eguchi, K. Nishijima (World Scientific, 1995)
L. Susskind, Phys. Rev. Lett. 23, 545 (1969)
L. Susskind, Phys. Rev. D. 1, 1182 (1970)
L. Susskind, Nuovo Cim. 69, 210 (1970)
H.B. Nielsen, Paper submitted to the 15th Int. Conf. on High Energy Physics, Kiev, 1970; Nordita Preprint (1969)
H.B. Nielsen, String from Veneziano model, arXiv:0904.4221v1 [hep-ph]
T. Goto, Prog. Theor. Phys. 46, 1560 (1971)
P.H. Frampton, Dual Resonance Models (W.A. Benjamin Inc, 1974)
P. Di Vecchia, The birth of string theory, arXiv:0704.0101v1 [hep-th]
N.D. Hari Dass, Lattice Theory for nonspecialists (1984), NIKHEF Preprint NIKHEF-H-84-11
L.D. Landau, E.M. lifshitz, Theory of Elasticity (Course of Theoretical Physics), vol. 7. (Elsevier Publishing Company, 1986)
E. Kretschmann, Ann. Phys. Leipzig. 53, 575 (1917)
N.D. Hari Dass, P. Matlock, (2007), arXiv:0709.1765 [hep-th]
N.D. Hari Dass, P. Matlock, Indian J. Phys. 88, 965 (2014)
Joseph Polchinski, Andrew Strominger, Phys. Rev. Lett. 67, 1681 (1991)
P. Goddard, J. Goldstone, C. Rebbi, C. Thorn, Nucl. Phys. B56, 109 (1973)
G. Barton, Introduction to advanced field theory, in Interscience Tracts on Physics and Astronomy, vol. 22 (1963)
S. Weinberg, The Quantum Theory of Fields-I (Cambridge University Press)
J.D. Bjorken, S. Drell, Relativistic Quantum Fields (McGraw Hill Publishers)
C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw Hill Publishers)
J. Polchinski, TASI lectures on D-branes, in Fields, Strings and Duality, TASI 1996 (World Scientific Publishers)
P.A.M. Dirac, Can. J. Math. 2, 129 (1950); Proc. R. Soc. A 246, 326 (1958)
R.C. Brower, Phys. Rev. D. 6, 1655 (1972)
P. Goddard, C.B. Thorn, Phys. Lett. B40, 235 (1972)
E. Del Guidice, P. Di Vecchia, S. Fubini, Ann. Phys. 70, 378 (1972)
M.A. Virasoro, Phys. Rev. D. 1, 2933 (1970)
J.F. Arvis, Phys. Lett. B. 127, 106 (1983)
L. Brink, P. Di Vecchia, P. Howe, Phys. Lett. B. 65, 471 (1976)
S. Deser, B. Zumino, Phys. Lett. B. 65, 369 (1976)
A.M. Polyakov, Phys. Lett. B. 103, 207 (1981)
N.D. Hari Dass, Hamiltonian formulation of Polyakov gravity, in Modern Quantum Field Theory, ed. by S. Das et al., (World Scientific, 1991)
J. Polchinski, String Theory, vol. 1. Cambridge University Press
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Hari Dass, N.D. (2023). The Birth of String Theory. In: Strings to Strings. Lecture Notes in Physics, vol 1018. Springer, Cham. https://doi.org/10.1007/978-3-031-35358-1_17
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