Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear canonical transformations and quantum phase:a unified canonical
  and algebraic approach   The algebra of generalized linear quantum canonical transformations is
examined in the prespective of Schwinger's unitary-canonical basis. Formulation
of the quantum phase problem within the theory of quantum canonical
transformations and in particular with the generalized quantum action-angle
phase space formalism is established and it is shown that the conceptual
foundation of the quantum phase problem lies within the algebraic properties of
the quantum canonical transformations in the quantum phase space. The
representations of the Wigner function in the generalized action-angle unitary
operator pair for certain Hamiltonian systems with the dynamical symmetry are
examined. This generalized canonical formalism is applied to the quantum
harmonic oscillator to examine the properties of the unitary quantum phase
operator as well as the action-angle Wigner function.

29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat