Volume 17, Issue 3, September 2010, Pages 257 - 279
A Hamiltonian Action of the Schrödinger–Virasoro Algebra on a Space of Periodic Time-Dependent Schrödinger Operators in (1 + 1)-Dimensions
Authors
Claude Roger
Institut Camille Jordan, Laboratoire associé au CNRS UMR 5208, Ecole Centrale de Lyon, INSA de Lyon, Université de Lyon Université Lyon I, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France
Jérémie Unterberger
Institut Elie Cartan, Laboratoire associé au CNRS UMR 7502, Université Henri Poincaré Nancy I, B.P. 239, F-54506 Vandoeuvre lès Nancy Cedex, France
Received 6 October 2008, Accepted 5 October 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000672How to use a DOI?
- Keywords
- Schrödinger–Virasoro Lie algebra; time-dependent Schrödinger operators; infinite-dimensional Lie algebras; algebra of pseudo-differential symbols; Poisson structure
- Abstract
Let be the space of Schrödinger operators in (1 + 1)-dimensions with periodic time-dependent potential. The action on 𝒮lin of a large infinite-dimensional reparametrization group SV with Lie algebra [8, 10], called the Schrödinger–Virasoro group and containing the Virasoro group, is proved to be Hamiltonian for a certain Poisson structure on 𝒮lin. More precisely, the infinitesimal action of appears to be part of a coadjoint action of a Lie algebra of pseudo-differential symbols, 𝔤, of which 𝔰𝔳 is a quotient, while the Poisson structure is inherited from the corresponding Kirillov–Kostant–Souriau form.
- Copyright
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Claude Roger AU - Jérémie Unterberger PY - 2021 DA - 2021/01/07 TI - A Hamiltonian Action of the Schrödinger–Virasoro Algebra on a Space of Periodic Time-Dependent Schrödinger Operators in (1 + 1)-Dimensions JO - Journal of Nonlinear Mathematical Physics SP - 257 EP - 279 VL - 17 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000672 DO - 10.1142/S1402925110000672 ID - Roger2021 ER -