Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Log-affine geodesics in the manifold of vector states on a von Neumann
  algebra
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas