# Transverse mode of a field

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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!

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nrqed
Homework Helper
Gold Member
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!
Yes, that's the definition. Note that you meant $\partial^\mu A^T_\mu(x)=0$.

Orodruin
Staff Emeritus
Note that you meant $\partial^\mu A^T_\mu(x)=0$.
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