139 Chapter 6: Heavy Quark Photon Production Radiation where, as usual, a bold variable represents a transverse two-vector. As a first step to compare to previously published results [305] we found the number distribution of emitted photons when simply plugging in massive 4- vectors into a standard classical E&M calculation: 6.2 Calculation where to get from the first to the second line we used the completeness relation ∑ λ =1 , $_{2}$ϵ µ $_{λ}$ϵ ν ∗ λ → − g$_{µν}$ , and where we took E$_{EM}$ = ∫ d $^{3}$k (2 π ) 3 e 2 2 ∑ λ =1 , 2 ∣ ∣ ⃗ϵ$_{λ}$ ( ⃗ k ) · ( ⃗ p ′ k · p ′ − ⃗ p k · p$^{)}$$^{∣}$ ∣ ∣ 2 (6.2) = ∫ d $^{3}$k (2 π ) 3 e 2 2 ( 2 p · p ′ ( k · p $^{′}$)( k · p ) − M 2 Q ( k · p $^{′}$) 2 − M 2 Q ( k · p ) 2 ) (6.3) ⇒ dN (0) E&M d $^{3}$k = Q $^{2}$α π $^{2}$ω (1 − x ) 2 k 2 + (1 − x ) $^{2}$m2 γ [ k 2 + (1 − x ) $^{2}$m2 γ + x $^{2}$M 2 $_{Q}$] 2 + O $^{(}$1 /E + $^{)}$, (6.4) p = [(1 − x ) E $^{+}$, M 2 Q + k 2 (1 − x ) E $_{+}$, − k ] (6.5) p ′ = [ M$_{Q}$ E $_{+}$, E$^{+}$, 0] (6.6) k = [ xE $^{+}$, m 2 γ + k 2 xE + , k ] , (6.7) with brackets indicating lightcone coordinates. There are two elements seen in Eq. (6.4) and not in Eq. (6.1): several