Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A topological approach to renormalization and its geometrical,
  dimensional consequences   The necessity of renormalization arises from the infinite integrals which are
caused by the discrepancy between the orders of differential and integral
operators in the four dimensional QFTs. Therefore in view of the fact that
finiteness and invariant properties of operators are their topological aspects,
essential renormalization tools to extract finite invariant values from those
infinities which are comparable with the experimental results, e. g.
regularization, perturbation and radiative corrections follow some topological
standards. In the second part we consider dimensional and geometrical
consequences of topological approach to renormalization for the geometrical
structure and degrees of freedom of renormalized theory. We show that
regularization and renormalization of QED are performed only by certain
restrictive dimensional conditions on QED fields. Further it is shown that in
accord with our previous topological approach to renormalization of QED the
geometrical evaluation of applied dimensional renormalization conditions and
the appearance of anomalies refer to a reduction of number of degrees of
freedom according to the reduced symmetry of QED. A conclusion concerning a
comparison of our results with holographic principle models is also included.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom