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Graphs in Perturbation Theory

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

This thesis is about graphs and two algebraic structures which can be associated with them. The first algebraic structure appears while enumerating large graphs. It captures the asymptotic behaviour of power series associated to graph counting problems. Second is the Hopf algebraic structure which gives an algebraic description of subgraph structures of graphs. The Hopf algebraic structure permits the explicit enumeration of graphs with constraints for the allowed subgraphs. Together both structures give an algebraic formulation of large graphs with forbidden subgraphs. The detailed analysis of both these structures is motivated by perturbative quantum field theory.

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Notes

  1. 1.

    Connected and bridgeless.

  2. 2.

    The asymptotic expansion of the coefficients of a first order asymptotic expansion is a second order asymptotic expansion and so on.

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Authors and Affiliations

  1. Departments of Physics and of Mathematics, Humboldt-Universität zu Berlin, Berlin, Germany

    Michael Borinsky

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  1. Michael Borinsky
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Correspondence to Michael Borinsky .

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Borinsky, M. (2018). Introduction. In: Graphs in Perturbation Theory. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-03541-9_1

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