The bialgebra of specified graphs and external structures (Q461271)
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scientific article; zbMATH DE number 6353601
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The bialgebra of specified graphs and external structures |
scientific article; zbMATH DE number 6353601 |
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The bialgebra of specified graphs and external structures (English)
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10 October 2014
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Summary: We construct a Hopf algebra structure on the space of specified Feynman graphs of a quantumfield theory. We introduce a convolution product and a semigroup of characters of this Hopf algebra with values in some suitable commutative algebra taking momenta into account. We then implement the renormalization described by \textit{A. Connes} and \textit{D. Kreimer} [Commun. Math. Phys. 210, No. 1, 249--273 (2000; Zbl 1032.81026)] and the Birkhoff decomposition for two renormalization schemes: the minimal subtraction scheme and the Taylor expansion scheme.
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bialgebra
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Hopf algebra
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Feynman graphs
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convolution product
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Birkhoff decomposition
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