Hi, the following is taken from Peskin and Schroeder page 36:(adsbygoogle = window.adsbygoogle || []).push({});

##\partial_{\mu}\phi(x) \rightarrow \partial_{\mu}(\phi(\Lambda^{-1}x)) = (\Lambda^{-1})^{\nu}_{\mu}(\partial_{\nu}\phi)(\Lambda^{-1}x)##

It describes the transformation law for a scalar field ##\phi(x)## for an active transformation.

I would like to work out the intermediate steps by myself as they are missing from the textbook. Can you please correct any mistakes I make?

##\partial_{\mu}\phi(x) \rightarrow \partial_{\mu}(\phi(\Lambda^{-1}x)) = \frac{\partial(\phi(\Lambda^{-1}x))}{\partial x^{\mu}} = \frac{\partial (\Lambda^{-1}x)^{\nu}}{\partial x^{\mu}} \frac{\partial \phi((\Lambda^{-1}x))}{\partial (\Lambda^{-1}x)^{\nu}} = (\Lambda^{-1})^{\nu}_{\mu}(\partial_{\nu}\phi)(\Lambda^{-1}x)##.

Am I correct?

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# Lorentz transformation of a scalar field

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