Lorentz Invariance of the Lagrangian

[Silviu]

Hello! I started reading stuff on QFT and it seems that one of the main points is for the Lagrangian to be Lorentz invariant, so that the equations of motion remain the same in all inertial reference frames. I am not sure however i understand how do non inertial reference frames come into play. I didn't take a course on GR yet, but Lorentz group doesn't accommodate accelerated linear motion for example, so a Lorentz scalar in one frame wouldn't be scalar in another frame moving with a non zero acceleration. So how is this taken into account, such that the equations of motion hold true in all frames?

 

[vanhees71]

As in Newtonian physics you can of course use non-inertial reference frames in SRT. You come already very close to the general tensor formalism needed in GR, and it's a good way to start into GR with this approach.

However, be warned, in QT non-inertial reference frames are not as easy as in classical physics, and particularly in QFT it's fascinating. E.g., if you just take a free field, quantize it in the usual way in an inertial frame and then ask, how the vacuum looks like for an accelerated observer, you get surprising results. E.g., taking a uniformly accelerated observer (i.e., with constant proper acceleration), you'll get the Unruh effect: The vacuum determined in the inertial frame (it's identical for all inertial frames because the vacuum is Poincare invariant) appears as a state with many particles in a thermal state for the acclerated observer (who lives in "Rindler space"). Look for "Unruh radiation".