Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Epstein-Glaser approach to pQFT: graphs and Hopf algebras   The paper aims at investigating perturbative quantum field theory (pQFT) in
the approach of Epstein and Glaser (EG) and, in particular, its formulation in
the language of graphs and Hopf algebras (HAs). Various HAs are encountered,
each one associated with a special combination of physical concepts such as
normalization, localization, pseudo-unitarity, causality and an associated
regularization, and renormalization. The algebraic structures, representing the
perturbative expansion of the S-matrix, are imposed on the operator-valued
distributions which are equipped with appropriate graph indices. Translation
invariance ensures the algebras to be analytically well-defined and graded
total symmetry allows to formulate bialgebras. The algebraic results are given
embedded in the physical framework, which covers the two recent EG versions by
Fredenhagen and Scharf that differ with respect to the concrete recursive
implementation of causality. Besides, the ultraviolet divergences occuring in
Feynman's representation are mathematically reasoned. As a final result, the
change of the renormalization scheme in the EG framework is modeled via a HA
which can be seen as the EG-analog of Kreimer's HA.

24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs