A promenade through singular symplectic geometry Authors Pablo Nicolás Martínez DOI: 10.2436/20.2002.02.43 Keywords: Poisson geometry, reduction, minimal coupling, Lie algebroid. Abstract In this article, we present symplectic and Poisson geometry from the perspective of Hamiltonian mechanics. We then introduce symplectic Lie algebroids, objects which lie between symplectic and Poisson manifolds. Afterwards, we recall the notion of symplectic reduction under the existence of a moment map. As an application of this construction, we describe the phase space of a charged particle interacting with a Yang–Mills field. Finally, we introduce a singular analogue of this construction and provide physical examples. Downloads Download data is not yet available. Downloads PDF How to Cite Nicolás Martínez, P. (2024). A promenade through singular symplectic geometry. Reports@SCM, 9(1), 65–76. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154342 More Citation Formats ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver Download Citation Endnote/Zotero/Mendeley (RIS) BibTeX Issue Vol. 9 No. 1 (2024) Section Articles License The intellectual property of articles belongs to the respective authors.On submitting articles for publication to the journal Reports@SCM, authors accept the following terms:Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Reports@SCM.Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.The journal Reports@SCM is not responsible for the ideas and opinions expressed by the authors of the published articles.
