Here is the anomalous dimension:
γΓ(t,g)=[∂∂tln(ZΓ(t,g))]t=1,
where
ZΓ is renormalization factor which arises in n-point functions
Γ,
t denotes change of renormalization parameter
t=μ′μ.
ZΓ arises explicitly after making shift of renormalization parameter
μ (for fixed type of renormalization):
Γ(xt,g)=Z−1Γ(t,g)Γ(x,ˉg(t,g)),x=kμ,t=μμ′.
Let's change type of regularization (coupling constant will change to g→˜g(g). Then n-point function will change as
Γ(kμ,g)=q(g)˜Γ(kμ,˜g(g)).
How to get from these equations that
γΓ will change to
˜γΓ(˜g(g))=γΓ(g)−β(g)dln(q(g))dg
(the definition for
β-function see
here)?
This post imported from StackExchange Physics at 2014-09-18 08:02 (UCT), posted by SE-user PhysiXxx