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## Main Question or Discussion Point

Hello! I am reading some QFT and at a point I read that any vector field (here we are working with massive spin 1 particles) can be written as: $$A_\mu(x)=A^T_\mu(x)+\partial_\mu\pi(x)$$ with $$\partial_\mu A^T_\mu(x)=0$$ They don't talk about notation, but from the context I understand that ##A^T_\mu(x)## is the transverse component of ##A_\mu(x)##. Is ##\partial_\mu A^T_\mu(x)=0## the definition of the transverse component? And if so, why? Thank you!