- Access by Xinjiang University
Dynamics Underlying Duality and Gauge Invariance in the Dual-Resonance Models
Phys. Rev. D 5, 2535 – Published 15 May, 1972
DOI: https://doi.org/10.1103/PhysRevD.5.2535
Abstract
Making use of the similarity between the factorized spectrum of the generalized beta function and the spectrum of a vibrating string in Minkowski space, we construct a formalism within which we give a geometrical interpretation to the gauge symmetries inherent in the theory. The key point in the construction is the identification of the harmonic-oscillator amplitude with the components of actual coordinates in space-time. It turns out that these coordinates must satisfy certain constraints arising from purely geometrical considerations, and these constraint equations are then shown to be the familiar gauge conditions on the underlying states. Analogies with more familiar gauge theories are pointed out.
References (18)
- R. Dolen, D. Horn, and C. Schmid, Phys. Rev. 166, 1768 (1968) R. Oehme, Nucl. Phys. B16, 161 (1970)
- G. Veneziano, Nuovo Cimento 57A, 190 (1968)
- Chan Hong-Mo, CERN Report No. CERN-TH-1057, 1969 (unpublished)
- S. Fubini and G. Veneziano, Nuovo Cimento 64A, 811 (1969) K. Bardakci and S. Mandelstam, Phys. Rev. 184, 1640 (1969)
Omitted endnote
- E. P. Wigner, Ann. Math. 40, 149 (1939)
- M. A. Virasoro, Phys. Rev. D 1, 2933 (1970)
- Y. Nambu, Univ. of Chicago Report No. EFI 70-70 (unpublished) in Copenhagen Lectures, 1971 (unpublished)
- Y. Nambu, in Symmetries and Quark Models, edited by R. Chand (Gordon and Breach, New York, 1970), p. 260
- S. Fubini, D. Gordon, and G. Veneziano, Phys. Letters 29B, 679 (1969) L. Susskind, Phys. Rev. D 1, 1182 (1970)
- Virasoro, [7]
Omitted endnote
- P. A. M. Dirac, Phys. Rev. 74, 817 (1948)
- L. P. Eisenhart, Riemannian Geometry (Princeton Univ. Press, Princeton, N. J., 1950)
- P. A. M. Dirac, Can. J. Math. 2, 147 (1950) P. A. M. DiracLectures on Quantum Mechanics (Academic, New York, 1964)
- Y. Nambu. P. Ramond, Phys. Rev. D 3, 2415 (1971)
- M. A. Virasoro, Phys. Rev. 177, 2309 (1969) J. Shapiro, Phys. Letters 33B, 361 (1970) G. Domokos, S. Kovesi-Domokos, and E. Schonberg, Phys. Rev. D 2, 1026 (1970)
- R. Penrose, J. Math. Phys. 8, 345 (1967)