Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase space trajectories in quantum mechanics   An adapted representation of quantum mechanics sheds new light on the
relationship between quantum states and classical states. In this approach the
space of quantum states splits into a product of the state space of classical
mechanics and a Hilbert space, and expectation values of observables decompose
into their classical value plus a quantum correction. The splitting is
preserved under time evolution of the Schr\"odinger equation under certain
assumptions, and the time evolution of the classical part of a quantum state is
governed by Hamilton's equation. The new representation is obtained from the
usual Hilbert space representation of quantum mechanics by introducing a gauge
degree of freedom in a time-dependent unitary transformation, followed by a
non-conventional gauge fixing condition.

1
The categories of this paper are: cs
18
The categories of this paper are: econ
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph