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arXiv · 1802.04362

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

Paul Skerritt
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Abstract

Recently Ohsawa has studied the Marsden-Weinstein-Meyer quotient of the manifold $T^*\mathbb{R}^n\times T^*\mathbb{R}^{2n^2}$ under a $\operatorname{O}(2n)$-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 $\mathcal{F}(T^*\mathbb{R}^n)$ of $T^*\mathbb{R}^n$. 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.

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Paul Skerritt. 2019-11-01. The frame bundle picture of Gaussian wave packet dynamics in semiclassical mechanics. https://doi.org/10.1007/s11005-019-01206-7

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