243 Appendix F: Heavy Quark Production Radiation Derivation arrive at We wish to calculate the field theory analog of the previous classical calcula- tions. Following Peskin pgs. 182-183 [251], consider the diagrams in Fig. F.2 contributing to bremsstrahlung radiation. E$_{Proca}$ = 2 k 0 2 ∑ λ =1 , 2 , 3 | ϵ$_{λ}$ · A| 2 = ∫ d $^{3}$k (2 π ) 3 e 2 2 ∑ λ =1 , 2 , 3 ∣ ∣ ϵ$_{λ}$ · ( p ′ k · p ′ − p k · p$^{)}$$^{∣}$ ∣ ∣ 2 (F.80) = ∫ d $^{3}$k (2 π ) 3 e 2 2 ( 2 p · p ′ ( k · p $^{′}$)( k · p ) − m 2 ( k · p $^{′}$) 2 − m 2 ( k · p ) 2 ) . (F.81) F.2 Field Theory Calculation F.2.1 Bremsstrahlung Radiation Figure F.2: Diagrams contributing to the probability of emitting a bremsstrahlung photon. Then, taking M$_{0}$ to denote the part of the amplitude that comes from the