Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization as a functor on bialgebras   The Hopf algebra of renormalization in quantum field theory is described at a
general level. The products of fields at a point are assumed to form a
bialgebra B and renormalization endows T(T(B)^+), the double tensor algebra of
B, with the structure of a noncommutative bialgebra. When the bialgebra B is
commutative, renormalization turns S(S(B)^+), the double symmetric algebra of
B, into a commutative bialgebra. The usual Hopf algebra of renormalization is
recovered when the elements of B are not renormalised, i.e. when Feynman
diagrams containing one single vertex are not renormalised. When B is the Hopf
algebra of a commutative group, a homomorphism is established between the
bialgebra S(S(B)^+) and the Faa di Bruno bialgebra of composition of series.
The relation with the Connes-Moscovici Hopf algebra of diffeomorphisms is
given. Finally, the bialgebra S(S(B)^+) is shown to give the same results as
the standard renormalisation procedure for the scalar field.

15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org