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In the equation (1.18) they omitted the translation vector $a^\mu$, but why?

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Am I correct that you added the a here? Because the index is wrong, you shouldn't have three mus in one expression, it has to be a sigma –  Noldig Feb 14 '13 at 15:24

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up vote 5 down vote accepted

Because a constant vector (like the translation vector) is annihilated by the differential operator $\partial^\mu$.

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