Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Space Quantum Mechanics on the Anti-De Sitter Spacetime and its
  Poincar\'e Contraction   In this work we propose an alternative description of the quantum mechanics
of a massive and spinning free particle in anti-de~Sitter spacetime, using a
phase space rather than a spacetime representation. The regularizing character
of the curvature appears clearly in connection with a notion of localization in
phase space which is shown to disappear in the zero curvature limit. We show in
particular how the anti-de~Sitter optimally localized (coherent) states
contract to plane waves as the curvature goes to zero. In the first part we
give a detailed description of the classical theory {\it \a la Souriau\/}. This
serves as a basis for the quantum theory which is constructed in the second
part using methods of geometric quantization. The invariant positive K\"ahler
polarization that selects the anti-de~Sitter quantum elementary system is shown
to have as zero curvature limit the Poincar\'e polarization which is no longer
K\"ahler. This phenomenon is then related to the disappearance of the notion of
localization in the zero curvature limit.

37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph