The Lagrangian of the Yang-Mills fields is given by
L=−14(Faμν)2+ˉψ(iγμDμ−m)ψ−12ξ(∂⋅Aa)2+ˉca(∂⋅Dab)cb
where the metric is
(−,+,+,+), and the conventions are the following:
[Dμ,Dν]=−igFμν,Dμ=∂μ−igAaμta,Dabμ=δab∂μ−gfabcAcμ
Let ϵ be an infinitesimal anticummuting parameter, and consider the BRST transformation:
δψ=igϵcataψ,δAaμ=ϵDabμcb,δca=−12gϵfabccbcc,δˉca=1ξϵ∂μAaμ
I have calculated the corresponding Noether current as
jμBRST=−gˉψγμcataψ−FaμνDabνcb−1ξ(∂⋅Aa)Dabμcb+12gfabc(∂μˉca)cbcc
I am not sure whether the result is correct or not, so I would like to check that ∂μjμBRST=0. Even though I have used the equation of motion
∂μFaμν=−gˉψγνtaψ−gfabcAbμFcμν−1ξ∂ν(∂⋅Aa)−gfabc(∂νˉcb)cc
(iγμDμ−m)ψ=0,∂μDabμcb=0
and spent about four hours, I still cannot get it right. Could someone help me check this? Thanks a lot.
This post imported from StackExchange Physics at 2014-07-03 17:59 (UCT), posted by SE-user soliton