Divergence of the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math></span>-Loop Planar Graph in the Dual-Resonance Model

Michio Kaku; Joël Scherk

doi:10.1103/PhysRevD.3.2000

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Divergence of the $N$ -Loop Planar Graph in the Dual-Resonance Model

Michio Kaku and Joël Scherk^*

Department of Physics, University of California, Berkeley, California 94720

^*N.A.T.O. Fellow on leave of absence from Laboratoire de Physique Theorique, Orsay, France.

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Phys. Rev. D 3, 2000 – Published 15 April, 1971

DOI: https://doi.org/10.1103/PhysRevD.3.2000

Abstract

Many of the results of a previous paper on the divergence of the two-loop planar graph are generalized to the multiloop case. In particular, the $N$ -loop amplitude is shown to diverge in at least $2^{N} - 1$ places, though no attempt is made to show that these are the only divergences. The implication of this result to the renormalization program is discussed.

References (8)

M. Kaku and L. P. Yu, LRL Report Nos. UCRL-20054, UCRL-20055, UCRL-20104, 1970 (unpublished) Phys. Letters 33B, 166 (1970)
C. Lovelace, Phys. Letters 32B, 703 (1970)
V. Alessandrini, CERN Report No. TH. 1215, 1970 (unpublished)
K. Kikkawa, B. Sakita, and M. A. Virasoro, Phys. Rev. 184, 1701 (1969)
M. Kaku and J. Scherk, Phys. Rev. D 3, 430 (1971)
D. J. Gross, A. Neveu, J. Scherk, and J. H. Schwarz, Phys. Rev. D 2, 697 (1970)
E. Cremmer and A. Neveu, Orsay report, 1970 (unpublished)
Omitted endnote

[c1] M. Kaku and L. P. Yu, LRL Report Nos. UCRL-20054, UCRL-20055, UCRL-20104, 1970 (unpublished) Phys. Letters 33B, 166 (1970)

[c2] C. Lovelace, Phys. Letters 32B, 703 (1970)

[c3] V. Alessandrini, CERN Report No. TH. 1215, 1970 (unpublished)

[c4] K. Kikkawa, B. Sakita, and M. A. Virasoro, Phys. Rev. 184, 1701 (1969)

[c5] M. Kaku and J. Scherk, Phys. Rev. D 3, 430 (1971)

[c6] D. J. Gross, A. Neveu, J. Scherk, and J. H. Schwarz, Phys. Rev. D 2, 697 (1970)

[c7] E. Cremmer and A. Neveu, Orsay report, 1970 (unpublished)

[c8] Omitted endnote

Physical Review D

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Divergence of the $N$ -Loop Planar Graph in the Dual-Resonance Model

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Divergence of the N-Loop Planar Graph in the Dual-Resonance Model

Abstract

References (8)

Divergence of the $N$ -Loop Planar Graph in the Dual-Resonance Model