Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards neutrino transport with flavor mixing in supernovae: the
  Liouville operator   The calculation of neutrino decoupling from nuclear matter requires a
transport formalism capable of handling both collisions and flavor mixing. The
first steps towards such a formalism are the construction of neutrino and
antineutrino "distribution matrices," and a determination of the Liouville
equations they satisfy in the noninteracting case. These steps are accomplished
through study of a Wigner-transformed "density function," the mean value of
paired neutrino quantum field operators.

3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci