Seminar talk, 21 October 2020: Difference between revisions
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| title = A converse to Noether's theorem | | title = A converse to Noether's theorem | ||
| abstract = The classical Noether's theorem states that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. It is a well-known statement to physicists with many applications. In the talk we investigate a reverse statement, namely that a differential equation which satisfies sufficiently many symmetries and corresponding conservation laws leads to a variational functional whose Euler-Lagrange equation is the given differential equation. The aim of the talk is to provide some background of the so-called inverse problem of the calculus of variations and then to discuss some new results, for example, how to prove the reverse statement. | | abstract = The classical Noether's theorem states that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. It is a well-known statement to physicists with many applications. In the talk we investigate a reverse statement, namely that a differential equation which satisfies sufficiently many symmetries and corresponding conservation laws leads to a variational functional whose Euler-Lagrange equation is the given differential equation. The aim of the talk is to provide some background of the so-called inverse problem of the calculus of variations and then to discuss some new results, for example, how to prove the reverse statement. | ||
| video = | |||
Language: English | |||
| video = https://video.gdeq.org/GDEq-zoom-seminar-20201021-Markus_Dafinger.mp4 | |||
| slides = | | slides = | ||
| references = | | references = {{arXiv|1906.10976}} | ||
| 79YY-MM-DD = 7979-89-78 | | 79YY-MM-DD = 7979-89-78 | ||
}} | }} | ||
Latest revision as of 08:40, 4 January 2025
Speaker: Markus Dafinger
Title: A converse to Noether's theorem
Abstract:
The classical Noether's theorem states that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. It is a well-known statement to physicists with many applications. In the talk we investigate a reverse statement, namely that a differential equation which satisfies sufficiently many symmetries and corresponding conservation laws leads to a variational functional whose Euler-Lagrange equation is the given differential equation. The aim of the talk is to provide some background of the so-called inverse problem of the calculus of variations and then to discuss some new results, for example, how to prove the reverse statement.
Language: English
Video
References:
arXiv:1906.10976