#### Title

#### Document Type

Preprint

#### Publication Date

4-11-2014

#### Publication Title

arXiv Repository

#### Abstract

Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any "large enough" subgroup G of Aut(L). This definition has two major drawbacks: when G=Aut(L) there are no known examples; and when G is a Lie subgroup the notion is, as we shall see, far from selective enough. In this paper we introduce the concept of a quantum state *localized at Y*, where Y is a coadjoint orbit of a subgroup H of G. We show that such states exist, and tend to be unique when Y has lagrangian preimage in X. This solves, in a number of cases, A. Weinstein's "fundamental quantization problem" of attaching state vectors to lagrangian submanifolds.

#### Recommended Citation

Ziegler, Francois.
2014.
"Localized Quantum States."
*arXiv Repository*: 1-29.
source: http://arxiv.org/abs/1310.7882

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/223

## Comments

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