Group weight and vanishing graphs

P. Butera; G. M. Cicuta; M. Enriotti

doi:10.1103/PhysRevD.21.972

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Group weight and vanishing graphs

P. Butera^*, G. M. Cicuta^*, and M. Enriotti^†

Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305

^*On leave from Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Italy.
^†On leave from Istituto di Fisica, Universita di Milano, Italy.

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Phys. Rev. D 21, 972 – Published 15 February, 1980

DOI: https://doi.org/10.1103/PhysRevD.21.972

Abstract

Various properties of the group weight of Feynman graphs in non-Abelian gauge theories are discussed. Infinitely many skeleton graphs with vanishing weight are exhibited for every compact Lie group. The $\frac{1}{N^{2}}$ dependence of the topological expansion is related to a $\frac{1}{N^{2}}$ expansion in some channels with the exchange of definite quantum numbers.

References (20)

P. Cvitanović, Phys. Rev. D 14, 1536 (1976)
G. Cicuta, Phys. Rev. Lett. 43, 826 (1979)
([4–8])
G. 't Hooft, Nucl. Phys. B72, 461 (1974)
G. Veneziano, Phys. Lett. 52B, 220 (1974) Nucl. Phys. B74, 365 (1974)
M. Ciafaloni, G. Marchesini, and G. Veneziano, Nucl. Phys. B98, 472 (1975) ibid.B98, 493 (1975)
G. P. Canning, Phys. Rev. D 12, 2505 (1975)
G. Chew and C. Rosenzweig, Phys. Rep. 41C, 263 (1978) E. Witten, Nucl. Phys. B160, 57 (1979)
E. WittenSec. 4 of Nakanishi's book, Graph Theory and Feynman Integrals (Gordon and Breach, New York, 1971)
Omitted endnote
([1])
P. Cvitanović, B. Lautrup, and R. Pearson, Phys. Rev. D 18, 1939 (1978)
Omitted endnote
J. Carazzone, E. Poggio, and H. Quinn, Phys. Rev. D 11, 2286 (1975)
N. Biggs, Algebraic Graph Theory (Cambridge University Press, Cambridge, 1974)
J. A. Bondy and U. S. R. Murty, Graph Theory with Applications (American Elsevier, New York, 1975), Appendix III
[1] P. Yeung, Phys. Rev. D 13, 2306 (1976)
Omitted endnote
Omitted endnote
A. J. MacFarlane, A. Sudbery, and P. H. Weisz, Commun. Math. Phys. 11, 77 (1968)

[c1] P. Cvitanović, Phys. Rev. D 14, 1536 (1976)

[c2] G. Cicuta, Phys. Rev. Lett. 43, 826 (1979)

[c3] ([4–8])

[c4] G. 't Hooft, Nucl. Phys. B72, 461 (1974)

[c5] G. Veneziano, Phys. Lett. 52B, 220 (1974) Nucl. Phys. B74, 365 (1974)

[c6] M. Ciafaloni, G. Marchesini, and G. Veneziano, Nucl. Phys. B98, 472 (1975) ibid.B98, 493 (1975)

[c7] G. P. Canning, Phys. Rev. D 12, 2505 (1975)

[c8] G. Chew and C. Rosenzweig, Phys. Rep. 41C, 263 (1978) E. Witten, Nucl. Phys. B160, 57 (1979)

[c9] E. WittenSec. 4 of Nakanishi's book, Graph Theory and Feynman Integrals (Gordon and Breach, New York, 1971)

[c10] Omitted endnote

[c11] ([1])

[c12] P. Cvitanović, B. Lautrup, and R. Pearson, Phys. Rev. D 18, 1939 (1978)

[c13] Omitted endnote

[c14] J. Carazzone, E. Poggio, and H. Quinn, Phys. Rev. D 11, 2286 (1975)

[c15] N. Biggs, Algebraic Graph Theory (Cambridge University Press, Cambridge, 1974)

[c16] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications (American Elsevier, New York, 1975), Appendix III

[c17] [1] P. Yeung, Phys. Rev. D 13, 2306 (1976)

[c18] Omitted endnote

[c19] Omitted endnote

[c20] A. J. MacFarlane, A. Sudbery, and P. H. Weisz, Commun. Math. Phys. 11, 77 (1968)

Physical Review D

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Group weight and vanishing graphs

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