TY - JOUR
T1 - Some aspects of the planar perturbation series
AU - Koplik, J.
AU - Neveu, A.
AU - Nussinov, S.
N1 - Funding Information:
* Research sponsored by the Energy Research and Development Administration, Grant no. E(ll-1) 2220-98. ** Address after April 1977: Ecole Normale Sup~rieure, Paris, France. *** Permanent address: Tel-Aviv University, Tel-Aviv, Israel.
PY - 1977/5/16
Y1 - 1977/5/16
N2 - We discuss several features of the class of planar Feynman diagrams in perturbation theory. We show that the number of planar n-loop diagrams grows exponentially in n in any field theory, and calculate the detailed asymptotic behavior for φ3 and φ4. We discuss the implications of this result for the convergence of the series and its relation to various semiclassical instabilities, with special reference to non-Abelian gauge theories. We also derive a functional integral equation for planar graphs.
AB - We discuss several features of the class of planar Feynman diagrams in perturbation theory. We show that the number of planar n-loop diagrams grows exponentially in n in any field theory, and calculate the detailed asymptotic behavior for φ3 and φ4. We discuss the implications of this result for the convergence of the series and its relation to various semiclassical instabilities, with special reference to non-Abelian gauge theories. We also derive a functional integral equation for planar graphs.
UR - http://www.scopus.com/inward/record.url?scp=33645934771&partnerID=8YFLogxK
U2 - 10.1016/0550-3213(77)90344-3
DO - 10.1016/0550-3213(77)90344-3
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AN - SCOPUS:33645934771
VL - 123
SP - 109
EP - 131
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
IS - 1
ER -