Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: ZM theory III: Classical oscillators and semi-classical Bohr-Sommerfeld
  quantization   We consider the description of classical oscillatory motion in ZM theory, and
explore the relationship of ZM theory to semi-classical Bohr-Sommerfeld
quantization. The treatment illustrates some features of ZM theory, especially
the inadequacies of classical and semi-classical treatments due to
non-analyticity of the mapping of classical trajectories onto the ZM clock
field. While the more complete ZM formalism is not developed here, the
non-analyticities in the classical treatment resemble issues in the comparison
of classical and quantum formalisms. We also show that semi-classical
quantization is valid for a periodic manifold in ZM theory, though the quantum
number $n=0$ is allowed, as it would be in quantum mechanics for a periodic
manifold. Still, this suggests a connection to the first-order success of Bohr
theory in describing the phenomenology of atomic quantum states. The
approximate nature of the semi-classical treatment of three dimensional atomic
orbits is, however, also apparent in relation to ZM theory. These observations
are preliminary to a discussion of ZM theory in relation to quantum mechanics
and quantum field theory in subsequent papers.

11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org