Action of the Lorentz group on scalar fields Thank you, just to write it on the original notation: $(g_2g_1)\phi(x)=\phi((\Lambda_2 \Lambda_1)^{-1} x)=\phi(\Lambda_1^{-1}\Lambda_2^{-1} x)$, and $g_2(g_1\phi)(x)=g_1\phi(\Lambda_2^{-1} x)= \phi(\Lambda_1^{-1}\Lambda_2^{-1} x)$