226 Appendix F: Heavy Quark Production Radiation Derivation Therefore We know that F 2 = 2( ⃗ B 2 + ⃗ E $^{2}$), and since E = − F 0 i we have that T EM µν = 2 √ − g δ δg µν [ − 1 4 √ − gg $^{αβ}$g$^{γδ}$F$_{αγ}$ F$_{βδ}$$^{]}$ = − 1 2 √ − g [ − √ − g 2 g$_{µν}$F 2 + √ − gδ α $_{µ}$δ β $_{ν}$g$^{γδ}$F$_{αγ}$ F$_{βδ}$ + √ − gg $^{αβ}$δγ $_{µ}$δ δ $_{ν}$F$_{αγ}$ F$_{βδ}$$^{]}$ = − 1 2 [ F$_{µγ}$F γ ν + F β $_{µ}$F$_{βν}$ − 1 2 g$_{µν}$F 2 ] = F$_{µλ}$F λ ν + 1 4 g$_{µν}$F$_{αβ}$F $^{αβ}$. (F.14) T 00 EM = F 0 $^{λ}$F 0 λ + 1 4 F 2 = F 0 $^{i}$F 0 i + 1 2 ( ⃗ B 2 − ⃗ E $^{2}$) = 1 2 ( ⃗ E 2 + ⃗ B $^{2}$) . (F.15) L$_{Proc}$ = L$_{EM}$ + µ 2 2 A $^{µ}$A$_{µ}$ (F.16) = − 1 4 F$_{µν}$F µν + µ 2 2 A $^{µ}$A$_{µ}$ (F.17) = − 1 4 g $^{αβ}$g$^{γδ}$F$_{αγ}$ F$_{βδ}$ + µ 2 2 g $^{αβ}$A$_{α}$ A$_{β}$, (F.18) Proca Let’s now find the stress-energy tensor for the Proca Lagrangian,