The QCD Quark Propagator in Coulomb Gauge and - Institut für Physik

Appendix A
Units and Conventions
In this work we use natural units, i.e.
= c = 1 .
(A.1)
A.1 Conventions in Minkowski space
In Minkowski space our metric is g = diag[1, −1, −1, −1]. A collection of relations for the
γ-matrices can be found in the appendix of [IZ]. They satisfy
{γ µ , γ ν } = 2 g µν . (A.2)
A.2 Euclidean conventions
In our Euclidean formulation:
p · q =
4∑
p i q i ;
(A.3)
i=1
{γ µ , γ ν } = 2 δ µν ; γ † µ = γ µ ; σ µν = i 2 [γ µ, γ ν ] ; tr[γ 5 γ µ γ ν γ ρ γ σ ] = −4 ǫ µνρσ , ǫ 1234 = 1 . (A.4)
A positive energy spinor satisfies
ū(P, s) (iγ · P + M) = 0 = (iγ · P + M) u(P, s) ,
(A.5)
where s = ± is the spin label. It is normalised:
ū(P, s) u(P, s) = 2M
(A.6)
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