The universal Hopf algebra of Feynman diagrams gives an efficient bookkeeping method for Feynman diagram calculations. Connes and Kreimer associated a Birkhoff decomposition to any character (e.g. Feynman rules) on this Hopf algebra. Birkhoff decompositions in loop groups are typically associated with solving Lax pair equations. We can reverse this process and find the Lax pair equation associated to the Connes-Kreimer decomposition. |
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