Transverse mode of a field

• I
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!

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