Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Jacobi fields in Hamiltonian mechanics   Jacobi fields of classical solutions of a Hamiltonian mechanical system are
quantized in the framework of vertical-extended Hamiltonian formalism. Quantum
Jacobi fields characterize quantum transitions between classical solutions.

28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph