Using this, the functional derivative in Eq. (1.32) is Note that the Faddeev-Popov method can be used to quantize QED, but there Eq. (1.34) does not depend on the photon field and hence it cannot introduce any new dynamics into the theory. However, in QCD the functional determinant explicitly depends on the gluon field A a $_{µ}$, because Eq. (1.34) contains the covariant derivative. The functional determinant that appears in (1.32) can be expressed in terms of a path integral involving Faddeev-Popov ghosts: The ghost fields c a and ¯ c a are unphysical, but are needed to defined the generating functional for the gluon field. The first term in L$_{gh}$ can be used to calculated the ghost propagator (given in Ref. [100], for instance) and the second term in L$_{gh}$ denotes an interaction between the ghost and gluon field. The delta functional appearing can be dealt with by multiplying the generating functional (1.32) by This is permitted because ω $^{a}$( x ) does not depend on the gluon field A a $_{µ}$, and hence multiplying the generating functional (1.32) by Eq. (1.36) can only alter the overall normalization of the generating functional. The delta function in (1.32) can be used to evaluate the integral (1.36). This effectively introduces a new term into the generating functional that has the form This is called the gauge-fixing Lagrangian, and a is the gauge parameter. Finally, the gener- 21 L$_{gf}$ = − 1 2 a ∂ $^{µ}$Aa $_{µ}$∂$^{ν}$A a ν . (1.37) exp$^{[}$ − i 2 a ∫ d $^{4}$x w $^{a}$( x ) w $^{a}$( x )$^{]}$ . (1.36) det$^{(}$ δG δθ ) = ∫ Dc D ¯ c exp$^{[}$ i$^{∫}$ d $^{4}$x L$_{gh}$$^{]}$ , L$_{gh}$ = ¯ c $^{a}$∂$^{µ}$Dab µ c b = − ∂ $^{µ}$¯ c $^{a}$∂$_{µ}$ c a + gf $^{abc}$Ac $_{µ}$∂$^{µ}$¯ c $^{a}$cb . (1.35) δG $^{a}$( x ) δθ $^{b}$( y ) = − ∂ $^{µ}$Dab µ δ $^{4}$( x − y ) . (1.34)