Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase operator problem and an index theorem for Q-deformed oscillator   The notion of index is applied to analyze the phase operator problem
associated with the photon. We clarify the absence of the hermitian phase
operator on the basis of an index consideration. We point out an interesting
analogy between the phase operator problem and the chiral anomaly in gauge
theory, and an appearance of a new class of quantum anomaly is noted. The
notion of index, which is invariant under a wide class of continuous
deformation, is also shown to be useful to characterize the representations of
Q-deformed oscillator algebra.

34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat