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Homework Statement
Hi everyone, in Peskin & Schroeder, P36, the derivative part of KG field is transformed as eqn (3.3). But why does the partial derivative itself not transform?
Homework Equations
[tex] \partial_{\mu} \phi (x) \rightarrow \partial_{\mu} ( \phi ( \Lambda^{-1} x) ) = ( \Lambda^{-1})^{\nu}_{\mu} (\partial_{\nu} \phi ) (\Lambda^{-1} x) [/tex]
The Attempt at a Solution
I thought the transformation was
[tex] \partial_{\mu} \phi (x) \rightarrow \Lambda^{\nu}_{\mu} \partial_{\nu} ( \phi ( \Lambda^{-1} x) ) =
\Lambda^{\nu}_{\mu}
( \Lambda^{-1})^{\lambda}_{\nu} (\partial_{\lambda} \phi ) (\Lambda^{-1} x) ? [/tex]
Thank you~