Noether's theorem for point particles

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Discussion Overview

The discussion centers around the exploration of Noether's theorem specifically in the context of point particle Lagrangian mechanics. Participants seek resources and literature that provide a detailed examination of this topic, noting the perceived lack of depth in standard textbooks.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that many textbooks do not cover Noether's theorem in detail for point particles and seeks recommendations for resources.
  • Another participant suggests that point particles can be modeled as Dirac delta-function distributions, implying that the continuum results of Noether's theorem are applicable.
  • A third participant mentions "Emily Noether's Wonderful Theorem" by Dwight Neuenschwander, expressing mixed feelings about its content, citing errors and a shaky mathematical approach, while acknowledging a lack of better alternatives.
  • Another participant recalls that Noether's theorem is likely discussed in Arnold's classical mechanics book and Marsden's work, but notes that these texts are heavily mathematical and cannot verify the content at the moment.

Areas of Agreement / Disagreement

Participants express a general agreement on the lack of comprehensive resources regarding Noether's theorem for point particles, but there are differing opinions on the quality and mathematical rigor of the available literature.

Contextual Notes

Some participants highlight limitations in the existing literature, including potential errors and the mathematical complexity of certain texts, which may affect understanding of Noether's theorem in this context.

William Crawford
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TL;DR
Literature recommendations for Noether's theorem for point particles.
Hi PF,

As I'm delving back into analytical mechanics, I've noticed that many textbooks don't provide an in-depth discussion of Noether's theorem in the context of point particle Lagrangian mechanics. Does anyone have recommendations for resources (books or otherwise) that cover this topic in detail?

Thanks!
 
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I believe the reason for this is that one can model point particles as Dirac delta-function distributions. Then the continuum results of Noether's theorem carry over directly.
 
William Crawford said:
TL;DR Summary: Literature recommendations for Noether's theorem for point particles.

Hi PF,

As I'm delving back into analytical mechanics, I've noticed that many textbooks don't provide an in-depth discussion of Noether's theorem in the context of point particle Lagrangian mechanics. Does anyone have recommendations for resources (books or otherwise) that cover this topic in detail?

Thanks!
"Emily Noether's Wonderful Theorem" by Dwight Neuenschwander is dedicated to Noether's theorem. I had mixed feelings about it. There were a number of gross errors and I thought the Rund-Trautmann approach was mathematically a bit shaky. That said, I'm not sure there's anything better. Most other textbooks skate through the theorem very quickly.
 
I'm almost certain it is treated in Arnold's classical mechanics book and Marsden's giant tome, but both of those references are very much on the mathematical side of things. I don't have either at hand to be able to verify.
 

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