A geometric derivation of Noether's theorem
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910847365808128 |
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| author | Houchmandzadeh, Bahram |
| author_facet | Houchmandzadeh, Bahram |
| contents | Noether's theorem is a cornerstone of analytical mechanics, making the link between symmetries and conserved quantities. In this article, I propose a simple, geometric derivation of this theorem that circumvents the usual difficulties that a student of this field usually encounters. The derivation is based on the direct use of the differential form $pdq -Hdt$, where $p$ is the momentum and $H$ the Hamiltonian, integrated over a simple curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19438 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A geometric derivation of Noether's theorem Houchmandzadeh, Bahram Classical Physics Noether's theorem is a cornerstone of analytical mechanics, making the link between symmetries and conserved quantities. In this article, I propose a simple, geometric derivation of this theorem that circumvents the usual difficulties that a student of this field usually encounters. The derivation is based on the direct use of the differential form $pdq -Hdt$, where $p$ is the momentum and $H$ the Hamiltonian, integrated over a simple curve. |
| title | A geometric derivation of Noether's theorem |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2502.19438 |