Dual Resonance Theory with Nonlinear Trajectories

M. Baker; D. D. Coon

doi:10.1103/PhysRevD.2.2349

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Dual Resonance Theory with Nonlinear Trajectories

M. Baker

D. D. Coon

Department of Physics, University of Washington, Seattle, Washington 98105

School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455

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Phys. Rev. D 2, 2349 – Published 15 November, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.2349

Abstract

A dual resonance model with nonlinear trajectories which includes the Veneziano model as a limiting case is discussed. Rules are given for constructing the $N$ -point function in such a model, and an explicit expression for the $N$ -point planar tree graph is derived. A conjectured rule for loop diagrams is also presented. Representations of four-point-function satellite terms which admit straightforward generalization to the $N$ -point function are derived.

Comments & Replies

Comments on a Dual Multiparticle Theory with Nonlinear Trajectories

M. Baker and D. D. Coon

Phys. Rev. D 4, 1234 (1971)

References (27)

G. Veneziano, Nuovo Cimento 57A, 190 (1968)
K. Kikkawa, B. Sakita, and M. A. Virasoro, Phys. Rev. 184, 1701 (1969)
S. Fubini, D. Gordon, and G. Veneziano, Phys. Letters 29B, 697 (1969) S. Fubini and G. Veneziano, Nuovo Cimento 64A, 811 (1969)
K. Bardakci, M. B. Halpern, and J. A. Shapiro, Phys. Rev. 185, 1910 (1969) K. Bardakci and M. B. Halpern, ibid. 183, 1456 (1969)
K. Kikkawa, Phys. Rev. 187, 2249 (1969) K. Kikkawa, S. Klein, B. Sakita, and M. Virasoro, Phys. Rev. D 1, 3258 (1970) D. Amati, C. Bouchiat, and J. Gervais, Nuovo Cimento Letters 2, 399 (1969) Y. Nambu, University of Chicago Report No. EFI 69-64 (unpublished) P. Olesen, Nucl. Phys. B18, 459 (1970) ibid.B18, 473 (1970) M. B. Green, Phys. Rev. 188, 2223 (1969) Phys. Rev. D 1, 450 (1970) J. C. Polkinghorne, Phys. Rev. 186, 1670 (1969) R. J. Rivers and J. J. G. Scanio, ibid. 188, 2170 (1969) T. H. Burnett and J. H. Schwartz, Phys. Rev. D 1, 423 (1970)
K. Bardakci and H. Ruegg, Phys. Letters 28B, 342 (1968) Phys. Rev. 181, 1884 (1969)
H.-M. Chan, Phys. Letters 28B, 425 (1969) H.-M. Chan and S. T. Tsou, ibid. 28B, 485 (1969)
C. Goebel and B. Sakita, Phys. Rev. Letters 22, 257 (1969)
M. Virasoro, Phys. Rev. Letters 22, 37 (1969) Z. Koba and H. Nielsen, Nucl. Phys. B10, 633 (1969)
D. Coon, Phys. Letters 29B, 669 (1969) Phys. Rev. 186, 1422 (1969) C. Lovelace, Phys. Letters 28B, 264 (1968) M. Ademollo, G. Veneziano, and S. Weinberg, Phys. Rev. Letters 22, 83 (1969)
M. Baker and D. D. Coon (unpublished)
L. Van Hove, Phys. Letters 24B, 183 (1967) L. Durand, III, Phys. Rev. 161, 1610 (1967)
R. L. Sugar and J. D. Sullivan, Phys. Rev. 166, 1515 (1968) R. Blankenbecler and R. L. Sugar, ibid. 168, 1597 (1968)
F. Capra, Phys. Letters 30B, 53 (1969)
Omitted endnote
J. E. Littlewood, Proc. London Math. Soc. 5, 361 (1907)
G. N. Watson, Trans. Cambridge Phil. Soc. 11, 281 (1910)
[2]
M. Baker and D. Coon (unpublished)
M. Baker and D. D. Coon (unpublished)
E. Heine, Handbuch der Kugelfunktionen (G. Riemer, Berlin, 1878)
F. H. Jackson, Am. J. Math. 32, 305 (1910) Quart. J. Pure Appl. Math. 41, 193 (1910) L. J. Slater ([25])
W. N. Bailey, Generalized Hypergeometric Series (Cambridge U. P., London, 1935)
D. B. Sears, Proc. London Math. Soc. (2) 53, 158 (1951) ibid.53, 181 (1951)
L. J. Slater, Generalized Hypergeometric Functions (Cambridge U. P., London, 1966) Higher Transcendental Functions, edited by A. Erdélyi (McGraw-Hill, New York, 1953), Vol. 1, p. 195
L. J. SlaterHigher Transcendental Functions ([25]), Vol. 1, p. 1
L. J. Slater, Rev. 25, p. 241

[c1] G. Veneziano, Nuovo Cimento 57A, 190 (1968)

[c2] K. Kikkawa, B. Sakita, and M. A. Virasoro, Phys. Rev. 184, 1701 (1969)

[c3] S. Fubini, D. Gordon, and G. Veneziano, Phys. Letters 29B, 697 (1969) S. Fubini and G. Veneziano, Nuovo Cimento 64A, 811 (1969)

[c4] K. Bardakci, M. B. Halpern, and J. A. Shapiro, Phys. Rev. 185, 1910 (1969) K. Bardakci and M. B. Halpern, ibid. 183, 1456 (1969)

[c5] K. Kikkawa, Phys. Rev. 187, 2249 (1969) K. Kikkawa, S. Klein, B. Sakita, and M. Virasoro, Phys. Rev. D 1, 3258 (1970) D. Amati, C. Bouchiat, and J. Gervais, Nuovo Cimento Letters 2, 399 (1969) Y. Nambu, University of Chicago Report No. EFI 69-64 (unpublished) P. Olesen, Nucl. Phys. B18, 459 (1970) ibid.B18, 473 (1970) M. B. Green, Phys. Rev. 188, 2223 (1969) Phys. Rev. D 1, 450 (1970) J. C. Polkinghorne, Phys. Rev. 186, 1670 (1969) R. J. Rivers and J. J. G. Scanio, ibid. 188, 2170 (1969) T. H. Burnett and J. H. Schwartz, Phys. Rev. D 1, 423 (1970)

[c6] K. Bardakci and H. Ruegg, Phys. Letters 28B, 342 (1968) Phys. Rev. 181, 1884 (1969)

[c7] H.-M. Chan, Phys. Letters 28B, 425 (1969) H.-M. Chan and S. T. Tsou, ibid. 28B, 485 (1969)

[c8] C. Goebel and B. Sakita, Phys. Rev. Letters 22, 257 (1969)

[c9] M. Virasoro, Phys. Rev. Letters 22, 37 (1969) Z. Koba and H. Nielsen, Nucl. Phys. B10, 633 (1969)

[c10] D. Coon, Phys. Letters 29B, 669 (1969) Phys. Rev. 186, 1422 (1969) C. Lovelace, Phys. Letters 28B, 264 (1968) M. Ademollo, G. Veneziano, and S. Weinberg, Phys. Rev. Letters 22, 83 (1969)

[c11] M. Baker and D. D. Coon (unpublished)

[c12] L. Van Hove, Phys. Letters 24B, 183 (1967) L. Durand, III, Phys. Rev. 161, 1610 (1967)

[c13] R. L. Sugar and J. D. Sullivan, Phys. Rev. 166, 1515 (1968) R. Blankenbecler and R. L. Sugar, ibid. 168, 1597 (1968)

[c14] F. Capra, Phys. Letters 30B, 53 (1969)

[c15] Omitted endnote

[c16] J. E. Littlewood, Proc. London Math. Soc. 5, 361 (1907)

[c17] G. N. Watson, Trans. Cambridge Phil. Soc. 11, 281 (1910)

[c18] [2]

[c19] M. Baker and D. Coon (unpublished)

[c20] M. Baker and D. D. Coon (unpublished)

[c21] E. Heine, Handbuch der Kugelfunktionen (G. Riemer, Berlin, 1878)

[c22] F. H. Jackson, Am. J. Math. 32, 305 (1910) Quart. J. Pure Appl. Math. 41, 193 (1910) L. J. Slater ([25])

[c23] W. N. Bailey, Generalized Hypergeometric Series (Cambridge U. P., London, 1935)

[c24] D. B. Sears, Proc. London Math. Soc. (2) 53, 158 (1951) ibid.53, 181 (1951)

[c25] L. J. Slater, Generalized Hypergeometric Functions (Cambridge U. P., London, 1966) Higher Transcendental Functions, edited by A. Erdélyi (McGraw-Hill, New York, 1953), Vol. 1, p. 195

[c26] L. J. SlaterHigher Transcendental Functions ([25]), Vol. 1, p. 1

[c27] L. J. Slater, Rev. 25, p. 241

Physical Review D

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Dual Resonance Theory with Nonlinear Trajectories

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Comments on a Dual Multiparticle Theory with Nonlinear Trajectories

References (27)

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