227 Appendix F: Heavy Quark Production Radiation Derivation where µ is the mass of the photon. Consider the variation of the new, massive photon part of the Lagrangian: Therefore And This agrees with Jackson problem 12.16 (a) [235]. Note that we recover T µν EM for µ → 0. E&M The E&M Lagrangian coupled to a classical source is F.1.3 Classical Bremsstrahlung Radiation L$_{E&M}$ = − 1 4 F $^{µν}$F$_{µν}$ − j $^{µ}$A$_{µ}$ . (F.22) T 00 Proca = 1 2$^{[}$ ⃗ E 2 + ⃗ B 2 + µ $^{2}$( A 0 2 + ⃗ A $^{2}$) $^{]}$. (F.21) T µν Proca = T µν EM + µ 2 ( A $^{µ}$Aν − 1 2 g $^{µν}$A$^{λ}$A$_{λ}$$^{)}$ = F $^{µλ}$F ν λ + 1 4 g $^{µν}$F$_{αβ}$ F αβ + µ 2 ( A $^{µ}$Aν − 1 2 g $^{µν}$A$^{λ}$A$_{λ}$$^{)}$ . (F.20) 2 √ − g δ δg µν $^{[}$µ 2 2 √ − gg $^{αβ}$A$_{α}$ A$_{β}$$^{]}$ = µ 2 √ − g$^{[}$ − √ − g 2 g$_{µν}$A 2 + √ − gA$_{µ}$A$_{ν}$$^{]}$ = µ 2 ( A$_{µ}$A$_{ν}$ − 1 2 g$_{µν}$A $^{λ}$A$_{λ}$$^{)}$ . (F.19)