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The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.
2
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Covariance of relativistic free particle Lagrangian under Lorentz transformation
I think while doing the calculations, I have found the answer. @GK gave an answer but I think there is a subtle mistake in that approach because both q and $\tau$ are coupled transformations of x and …
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1
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Covariance of relativistic free particle Lagrangian under Lorentz transformation
How does the Lagrangian of a free particle:
$$ L = - \sqrt{1- \Big(\frac{dx}{dt}\Big)^{2}} $$
transform under the co-ordinate transformation $(q,\tau)$?
$$ q = \cosh(\psi)x + \sinh(\psi)t, $ …