{"title":"勘误:$ k $-余辛框架下奇异场论的约束算法","authors":"Xavier Gràcia, X. Rivas, N. Rom'an-Roy","doi":"10.3934/JGM.2020002","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of \\begin{document}$ k $\\end{document} -cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of \\begin{document}$ k $\\end{document} -precosymplectic structure, which is a generalization of the \\begin{document}$ k $\\end{document} -cosymplectic structure. Next \\begin{document}$ k $\\end{document} -precosymplectic Hamiltonian systems are introduced in order to describe singular field theories, both in Lagrangian and Hamiltonian formalisms. Finally, we develop a constraint algorithm in order to find a submanifold where the existence of solutions of the field equations is ensured. The case of affine Lagrangians is studied as a relevant example.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"95 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2018-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Erratum: Constraint algorithm for singular field theories in the $ k $-cosymplectic framework\",\"authors\":\"Xavier Gràcia, X. Rivas, N. Rom'an-Roy\",\"doi\":\"10.3934/JGM.2020002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of \\\\begin{document}$ k $\\\\end{document} -cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of \\\\begin{document}$ k $\\\\end{document} -precosymplectic structure, which is a generalization of the \\\\begin{document}$ k $\\\\end{document} -cosymplectic structure. Next \\\\begin{document}$ k $\\\\end{document} -precosymplectic Hamiltonian systems are introduced in order to describe singular field theories, both in Lagrangian and Hamiltonian formalisms. Finally, we develop a constraint algorithm in order to find a submanifold where the existence of solutions of the field equations is ensured. The case of affine Lagrangians is studied as a relevant example.\",\"PeriodicalId\":49161,\"journal\":{\"name\":\"Journal of Geometric Mechanics\",\"volume\":\"95 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2018-12-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Geometric Mechanics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/JGM.2020002\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geometric Mechanics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/JGM.2020002","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 4
摘要
The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of \begin{document}$ k $\end{document} -cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of \begin{document}$ k $\end{document} -precosymplectic structure, which is a generalization of the \begin{document}$ k $\end{document} -cosymplectic structure. Next \begin{document}$ k $\end{document} -precosymplectic Hamiltonian systems are introduced in order to describe singular field theories, both in Lagrangian and Hamiltonian formalisms. Finally, we develop a constraint algorithm in order to find a submanifold where the existence of solutions of the field equations is ensured. The case of affine Lagrangians is studied as a relevant example.
Erratum: Constraint algorithm for singular field theories in the $ k $-cosymplectic framework
The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of \begin{document}$ k $\end{document} -cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of \begin{document}$ k $\end{document} -precosymplectic structure, which is a generalization of the \begin{document}$ k $\end{document} -cosymplectic structure. Next \begin{document}$ k $\end{document} -precosymplectic Hamiltonian systems are introduced in order to describe singular field theories, both in Lagrangian and Hamiltonian formalisms. Finally, we develop a constraint algorithm in order to find a submanifold where the existence of solutions of the field equations is ensured. The case of affine Lagrangians is studied as a relevant example.
期刊介绍:
The Journal of Geometric Mechanics (JGM) aims to publish research articles devoted to geometric methods (in a broad sense) in mechanics and control theory, and intends to facilitate interaction between theory and applications. Advances in the following topics are welcomed by the journal:
1. Lagrangian and Hamiltonian mechanics
2. Symplectic and Poisson geometry and their applications to mechanics
3. Geometric and optimal control theory
4. Geometric and variational integration
5. Geometry of stochastic systems
6. Geometric methods in dynamical systems
7. Continuum mechanics
8. Classical field theory
9. Fluid mechanics
10. Infinite-dimensional dynamical systems
11. Quantum mechanics and quantum information theory
12. Applications in physics, technology, engineering and the biological sciences.