Document Type
Presentation
Presentation Date
11-8-2014
Abstract or Description
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."
Department of 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