Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorics of (perturbative) quantum field theory   We review the structures imposed on perturbative QFT by the fact that its
Feynman diagrams provide Hopf and Lie algebras. We emphasize the role which the
Hopf algebra plays in renormalization by providing the forest formulas. We
exhibit how the associated Lie algebra originates from an operadic operation of
graph insertions. Particular emphasis is given to the connection with the
Riemann--Hilbert problem. Finally, we outline how these structures relate to
the numbers which we see in Feynman diagrams.

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The categories of this paper are: stat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics