I've been slowly self studying Lagrangian topics, and have gotten to Noether's theorem.(adsbygoogle = window.adsbygoogle || []).push({});

I've tried application of a Lorentz boost to all the terms in the Lorentz force Lagrangian (which is invariant with respect to boost since it has only four vector dot products). Then using Noether's theorem to find the invariant with respect to the boost rapidity I eventually end up with the following pair of vector equations:

[tex]

- ct \frac{d (\gamma \mathbf{p})}{dt} + \mathbf{x} \frac{d (m c \gamma)}{dt} = \frac{q}{c} \frac{d \left( -ct \mathbf{A} + \phi \mathbf{x} \right) }{dt}

[/tex]

[tex]

\mathbf{x} \times \frac{d( \gamma \mathbf{p} )}{dt} = \frac{q}{c} \frac{d}{dt} \left( \mathbf{x} \times \mathbf{A} \right)

[/tex]

I've made up the exersize for myself so I have no back of the book solutions to check against.

Has anybody seen something like this before, and if so did I get the right result?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Application of Noethers to Lorentz force Lagrangian with boost

**Physics Forums | Science Articles, Homework Help, Discussion**