## 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.

Original language | American English |
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State | Published - Nov 8 2014 |

Event | Gone Fishing: Poisson Geometry Conference - Berkeley, United States Duration: Nov 8 2014 → Nov 9 2014 |

### Conference

Conference | Gone Fishing |
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Country/Territory | United States |

City | Berkeley |

Period | 11/8/14 → 11/9/14 |

## Keywords

- Coadjoint orbit
- Kostant-Souriau line
- Lagrangian submanifolds
- Quantum state
- State vectors
- Symplectic manifold

## DC Disciplines

- Mathematics
- Physical Sciences and Mathematics