Special relativity in Lagrangian and Hamiltonian language

[lriuui0x0]

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.

 

[PeroK]

There is Susskind's Special Relativity and Classical Field Theory.

 

[George Jones]

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.

 

[lriuui0x0]

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.

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.

 

[robphy]

Possible interesting:

Doughty, Lagrangian Interaction
https://www.amazon.com/dp/0201416255/?tag=pfamazon01-20

Abraham and Marsden, Foundations of Mechanics
https://authors.library.caltech.edu/25029/

Jose and Saletan, Classical Dynamics: A Contemporary Approach
https://www.amazon.com/dp/0521636361/?tag=pfamazon01-20

Sudarshan and Makunda, Classical Dynamics: A Modern Perspective
https://www.amazon.com/dp/9814730017/?tag=pfamazon01-20

 

[andresB]

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

 

[vanhees71]

Here's my attempt to explain SRT, including a lot of action-principle arguments (though in Lagrangian form, because there everything is manifestly covariant ;-)):

https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf

 

[paralleltransport]

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).