Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Four-wave interaction in gas and vacuum: definition of a third-order
  nonlinear effective susceptibility in vacuum: $\chi$ vacuum(3)   Semiclassical methods are used to study the nonlinear interaction of light in
vacuum in the context of four wave mixing. This study is motivated by a desire
to investigate the possibility of using recently developed powerful ultrashort
(femtosecond) laser pulses to demonstrate the existence of nonlinear effects in
vacuum, predicted by quantum electrodynamics (QED). An approach, similar to
classical nonlinear optics in a medium, is developed in this article. A
third-order nonlinear effective susceptibility of vacuum is then introduced.

37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat