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Quantum field theory and the coloring problem of graphs

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Abstract

The φk theory is compared with the multilinear theory of scalar fields φ1, φ2, ..., φ k having the same mass as that of φ. In particular, it is shown that Feynman integrals encountered in the φ3 theory are not necessarily present also in the φ1 φ2 φ3 theory, but they are if they correspond to planar Feynman graphs having no tadpole part. Furthermore, a necessary and sufficient condition for the presence of a φ3 Feynman integral in the φ1 φ 22 theory is found. Those considerations are applications of graph theory, especially of the coloring problem of graphs, to Feynman graphs.

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References

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    Noboru Nakanishi

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  1. Noboru Nakanishi
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Nakanishi, N. Quantum field theory and the coloring problem of graphs. Commun.Math. Phys. 32, 167–181 (1973). https://doi.org/10.1007/BF01645654

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  • DOI: https://doi.org/10.1007/BF01645654

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