Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Local Ward identities for collective excitations in fermionic systems
  with spontaneously broken symmetries
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph