Relativity Special relativity in Lagrangian and Hamiltonian language

AI Thread Summary
The discussion centers on finding books that introduce Lagrangian and Hamiltonian mechanics within the context of special relativity, highlighting the need for a mathematical formalism rather than a classical mechanics framework. Recommendations include Eric Gourgoulhon's "Special Relativity in General Frames," which covers the principle of least action at a graduate level, and Susskind's "Special Relativity and Classical Field Theory." Other suggested texts include "Lagrangian Interaction" by Doughty, "Foundations of Mechanics" by Abraham and Marsden, and "Classical Dynamics: A Contemporary Approach" by Jose and Saletan. The conversation also touches on the utility of QFT textbooks for concise treatments of these topics, with Landau and Lifshitz's volume 2 noted for its accessible approach to relativity from a Lagrangian perspective. Overall, the thread emphasizes the importance of mathematical rigor in understanding the relationship between classical and relativistic mechanics.
lriuui0x0
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Some introduction books on Lagrangian and Hamiltonian mechanics use classical mechanics as the theoretical framework, and when it come to special relativity it goes back to the basics and force language again. I would like to ask for some recommendations on good books that introduces Lagrangian and Hamiltonian mechanics in the special relativity settings, especially some notes on their relationship with the classical mechanics counterpart would be great! E.g. Neother's theorem in special relativity.
 
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There is Susskind's Special Relativity and Classical Field Theory.
 
lriuui0x0 said:
I would like to ask for some recommendations on good books that introduces Lagrangian and Hamiltonian mechanics in the special relativity settings, especially some notes on their relationship with the classical mechanics counterpart would be great! E.g. Neother's theorem in special relativity.
At what level? At the graduate student level, there is chapter 11 "Principle of Least Action" from the beautiful book "Special Relativity in General Frames" by Eric Gourgoulhon.
 
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George Jones said:
At what level? At the graduate student level, there is chapter 11 "Principle of Least Action" from the beautiful book "Special Relativity in General Frames" by Eric Gourgoulhon.
That's a really good recommendation! I wonder if there're classical mechanics books that follows a similar philosophy? E.g. starting from a mathematical formulism in coordinate free language.

PeroK said:
There is Susskind's Special Relativity and Classical Field Theory.
Thanks! I watched Susskind's lectures before but I'm looking for something with a bit more mathematical formalism.
 
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Analytical Mechanics for Relativity and Quantum Mechanics​

https://www.amazon.com/dp/0198766807/?tag=pfamazon01-20Of possible interest

  • A direct derivation of the relativistic Lagrangian for a system of particles using d'Alembert's principle

https://aapt.scitation.org/doi/10.1119/1.4885349

Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems​

https://iopscience.iop.org/article/10.1088/0305-4470/38/6/006

https://web-docs.gsi.de/~struck/hp/hamilton/hamilton2.pdf
 
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Interestingly, the most concise and elegant treatments I know come from QFT textbooks. This is useful only if you are already familiar with calculus of variations.

Example: Peskin & schroeder section 2.2
http://www.fulviofrisone.com/attachments/article/483/Peskin, Schroesder - An introduction To Quantum Field Theory(T).pdf

At a more elementary level, Landau Lifshitz vol. 2 (also available free online) treats relativity very well starting from the lagrangian perspective, section 8.
http://fulviofrisone.com/attachments/article/209/Landau L.D. Lifschitz E.M.- Vol. 2 - The Classical Theory of Fields.pdf

For more elementary treatments I don't quite have a good reference unfortunately. Maybe you can tell use how much physics math you have studied (undergrad physics degree?). Landau vol.2 can be understood if you have the equivalent of vol. 1 (undergrad level classical mechanics).
 
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