225 Appendix F: Heavy Quark Production Radiation Derivation Therefore we find an identity we will use often in the following: similarly We will use variation with respect to the metric to find the (automatically) symmetric, gauge-invariant form of T µν [319]: δ √ − g δg µν = 1 2 √ − g gg$_{µν}$ = − √ − g 2 g$_{µν}$ ; (F.10) δ √ − g δg$_{µν}$ = √ − g 2 g $^{µν}$. (F.11) T$_{µν}$ = 2 √ − g δ √ − g L δg µν , (F.12) F.1.2 T µν from Varying the Metric E&M where g is the determinant of the metric and the coefficient out front gives the proper normalization for the usual stress-energy tensor (assuming a + − −− type metric). As a warmup exercise we use Eq. (F.12) to derive the usual E&M energy density from its Lagrangian, L$_{EM}$ = − 1 4 F$_{µν}$F µν = − 1 4 g $^{αβ}$g$^{γδ}$F$_{αγ}$ F$_{βδ}$. (F.13)