Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Polar Duality and the Symplectic Camel: a Geometric Approach to
  Quantization   We define and study the notion of quantum polarity, which is a kind of
geometric Fourier transform between sets of positions and sets of momenta.
Extending previous work of ours, we show that the orthogonal projections of the
covariance ellipsoid of a quantum state on the configuration and momentum
spaces form what we call a dual quantum pair. We thereafter show that quantum
polarity allows solving the Pauli reconstruction problem for Gaussian
wavefunctions. The notion of quantum polarity exhibits a strong interplay
between the uncertainty principle and symplectic and convex geometry and our
approach could therefore pave the way for a geometric and topological version
of quantum indeterminacy. We relate our results to the Blaschke-Santal\'o
inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty
principle and the less-known Donoho--Stark principle from the point of view of
quantum polarity.

32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom