2
$\begingroup$

I am reading Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries by Sylvain Marsat.

In section 2B the author imposes the invariance of the Lagrangian under infinitesimal coordinate transformations: which is the physical menaing of this?

$\endgroup$
2
$\begingroup$

Rather than asking why we should impose this invariance, I think it would make more sense to ask why we should relax it. The Lagrangian is a relativistic scalar, which means that it has to be invariant under any coordinate transformation. An infinitesimal change of coordinates is just one type of coordinate transformation.

The physical interpretation is that coordinates don't in general have a physical interpretation. Coordinates are just names. A change of coordinates is just a renaming of points in spacetime. If we're going to derive equations of motion from a Lagrangian, we want those equations of motion to be true regardless of how we rename points in spacetime.

$\endgroup$
-2
$\begingroup$

Invariance under certain transformations mean conserved physical properties.

$\endgroup$
  • 1
    $\begingroup$ That doesn't apply here. Diffeomorphism invariance doesn't yield anything nontrivial when you apply Noether's theorem to it. $\endgroup$ – Ben Crowell Oct 21 at 13:45
  • $\begingroup$ Maybe I should have read the section. Thanks. $\endgroup$ – Jan2103 Oct 21 at 13:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.