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The frame bundle picture of Gaussian wave packet dynamics in semiclassical mechanics

Skerritt, Paul (2019) The frame bundle picture of Gaussian wave packet dynamics in semiclassical mechanics Letters in Mathematical Physics, 109 (12). pp 2723-2751.

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Recently Ohsawa (Lett Math Phys 105:1301–1320, 2015) has studied the Marsden–Weinstein–Meyer quotient of the manifold T ∗Rn × T ∗R2n2 under a O(2n)-symmetry and has used this quotient to describe the relationship between two different parametrisations of Gaussian wave packet dynamics commonly used in semiclassical mechanics. In this paper, we suggest a new interpretation of (a subset of) the unreduced space as being the frame bundle F(T ∗Rn) of T ∗Rn. We outline some advantages of this interpretation and explain how it can be extended to more general symplectic manifolds using the notion of the diagonal lift of a symplectic form due to Cordero and de León (Rend Circ Mat Palermo 32:236–271, 1983).

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : December 2019
Funders : The Leverhulme Trust Research Project
DOI : 10.1007/s11005-019-01206-7
Copyright Disclaimer : © The Author(s) 2019. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Uncontrolled Keywords : Frame bundle; Dual pair; Symplectic reduction; Semiclassical mechanics; Gaussian wave packet
Additional Information : The author is grateful to Tomoki Ohsawa, Cesare Tronci, Manuel de León, Cornelia Vizman, Darryl Holm and Martin Wolf for useful discussions, and to the reviewer for helpful comments. This work was supported by the Leverhulme Trust Research Project Grant 2014-112 and the Institute of Mathematics and its Applications Small Grant Scheme.
Depositing User : Diane Maxfield
Date Deposited : 12 Nov 2019 15:25
Last Modified : 14 Sep 2020 02:08

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