Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collective behavior of light in vacuum   Under the action of light-by-light scattering, light beams show collective
behaviors in vacuum. For instance, in the case of two counterpropagating laser
beams with specific initial helicity, the polarization of each beam oscillates
periodically between the left and right helicity. Furthermore, the amplitudes
and the corresponding intensities of each polarization propagate like waves.
Such polarization waves might be observationally accessible in future laser
experiments, in a physical regime complementary to those explored by particle
accelerators.

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an