Graduate What Is the Renormalized Gluon Dressing Function?

[RicardoMP]

Consider, for example, the gluon propagator $$D^{\mu\nu}(q)=-\frac{i}{q^2+i\epsilon}[D(q^2)T^{\mu\nu}_q+\xi L^{\mu\nu}_q]$$

What exactly is the renormalized gluon dressing function $D(q^2)$ and what is its definition? My interest is in knowing if I can then write the bare version of this function simply as $D_B(q^2)=Z_AD(q^2)$, where $Z_A$ is the renormalization constant for the gluon field ($A_B=Z_A^{\frac{1}{2}}A$).

 

[azntoon]

The renormalized gluon dressing function $D(q^2)$ is defined as the inverse of the renormalized gluon propagator, which can be written as: $$D^{\mu\nu}(q)=-i[D(q^2)T^{\mu\nu}_q+\xi L^{\mu\nu}_q]$$where $T^{\mu\nu}_q$ and $L^{\mu\nu}_q$ are the transverse and longitudinal tensors, respectively, and $\xi$ is the gauge parameter. The renormalized gluon dressing function is then defined as$$D(q^2)=\frac{1}{-i(T^{\mu\nu}_q+\xi L^{\mu\nu}_q)D^{\mu\nu}(q)}$$Yes, you can write the bare version of the function as $D_B(q^2)=Z_AD(q^2)$, where $Z_A$ is the renormalization constant for the gluon field ($A_B=Z_A^{\frac{1}{2}}A$).