#### Document Type

Presentation

#### Publication Date

11-8-2014

#### 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 far from selective enough. In this talk I’ll introduce the concept of a quantum state *localized at Y *, where Y is a coadjoint orbit of a subgroup H of G. I’ll explain how such states often exist and are unique when Y has lagrangian preimage in X, and how this can be regarded as a solving, in a number of cases, A. Weinstein’s “fundamental quantization problem” of attaching state vectors to lagrangian submanifolds.

#### Sponsorship/Conference/Institution

Gone Fishing Conference on Poisson Geometry

#### Location

Berkeley, CA

#### Source

https://math.berkeley.edu/~libland/gone-fishing-2014/ziegler.pdf

#### Recommended Citation

Ziegler, François.
2014.
"Quantum States Localized on Lagrangian Submanifolds."
*Mathematical Sciences Faculty Presentations*.
Presentation 6.
source: https://math.berkeley.edu/~libland/gone-fishing-2014/ziegler.pdf

https://digitalcommons.georgiasouthern.edu/math-sci-facpres/6