Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Hamiltonian Formulation of the Pais-Uhlenbeck Oscillator that Yields a
  Stable and Unitary Quantum System   We offer a new Hamiltonian formulation of the classical Pais-Uhlenbeck
Oscillator and consider its canonical quantization. We show that for the
non-degenerate case where the frequencies differ, the quantum Hamiltonian
operator is a Hermitian operator with a positive spectrum, i.e., the quantum
system is both stable and unitary. A consistent description of the degenerate
case based on a Hamiltonian that is quadratic in momenta requires its analytic
continuation into a complex Hamiltonian system possessing a generalized
PT-symmetry (an involutive antilinear symmetry). We devise a real description
of this complex system, derive an integral of motion for it, and explore its
quantization.

29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph