Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vacuum polarization tensor in inhomogeneous magnetic fields   We develop worldline numerical methods, which combine string-inspired with
Monte-Carlo techniques, for the computation of the vacuum polarization tensor
in inhomogeneous background fields for scalar QED. The algorithm satisfies the
Ward identity exactly and operates on the level of renormalized quantities. We
use the algorithm to study for the first time light propagation in a spatially
varying magnetic field. Whereas a local derivative expansion applies to the
limit of small variations compared to the Compton wavelength, the case of a
strongly varying field can be approximated by a derivative expansion for the
averaged field. For rapidly varying fields, the vacuum-magnetic refractive
indices can exhibit a non-monotonic dependence on the local field strength.
This behavior can provide a natural limit on the self-focussing property of the
quantum vacuum.

32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio