Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete evolution for the zero-modes of the Quantum Liouville Model   The dynamical system for the zero modes of the Liouville Model, which is
separated from the full dynamics for the discrete shifts of time $ t \to t +
\pi $, is investigated. The structure of the modular double in quantum case is
introduced.

19
The categories of this paper are: eess
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex