The corresponding expression for I$_{VP}$ ( ω ) in the Feynman gauge can be found, e.g., in Ref. [58]. The contribution of this diagram reads The contribution of the diagram D is given by the expression where the operator I ml VP can be derived within the two-time Green function method. In the present work we omit this term, assuming its value is relatively small. The reducible contributions G , H and I are given by Δ E VP( F ) SQED = 2 ∑ n 1 ′ 〈 Pa | T$_{0}$ | n$_{1}$ 〉 ε$_{Pa}$ − ε$_{n}$$_{1}$ 〈 n$_{1}$Pb | I$_{VP}$ (Δ) | QaQb 〉 . (59) Δ E VP( D ) SQED = 〈 PaPb | I ml $_{VP}$(Δ) | QaQb 〉 , (60) Δ E VP( G ) SQED = Δ E VP( G 1) SQED + Δ E VP( G 2) SQED + Δ E VP( G 3) SQED , (61) Δ E VP( G 1) SQED = − 2 ∑ n 1 ′ 1 ( ε$_{Pa}$ − ε$_{n}$$_{1}$ ) 2 { 〈 Pa | U el VP | n$_{1}$ 〉〈 n$_{1}$ | T$_{0}$ | Pa 〉〈 PaPb | I (Δ) | QaQb 〉 + 〈 Pa | U el VP | Pa 〉〈 Pa | T$_{0}$ | n$_{1}$ 〉〈 n$_{1}$Pb | I (Δ) | QaQb 〉 + 〈 Pa | T$_{0}$ | Pa 〉〈 Pa | U el VP | n$_{1}$ 〉〈 n$_{1}$Pb | I (Δ) | QaQb 〉 } , (62) Δ E VP( G 2) SQED = 2 { ∑ n 1 ′ 1 ε$_{Pa}$ − ε$_{n}$$_{1}$ [ 〈 Pa | U el VP | n$_{1}$ 〉〈 n$_{1}$ | T$_{0}$ | Pa 〉〈 PaPb | I $^{′}$(Δ) | QaQb 〉 + 〈 Pa | U el VP | n$_{1}$ 〉〈 n$_{1}$Pb | I $^{′}$(Δ) | QaQb 〉 ( 〈 Qb | T$_{0}$ | Qb 〉 − 〈 Pb | T$_{0}$ | Pb 〉 )] + 〈 Pa | U el VP | Pa 〉 [ ∑ n 1 ′ 〈 PaPb | I $^{′}$(Δ) | n$_{1}$Qb 〉〈 n$_{1}$ | T$_{0}$ | Qa 〉 ε$_{Qa}$ − ε$_{n}$$_{1}$ + ∑ n 1 ′ 〈 PaPb | I $^{′}$(Δ) | Qan$_{1}$ 〉〈 n$_{1}$ | T$_{0}$ | Qb 〉 ε$_{Qb}$ − ε$_{n}$$_{1}$ ]} , (63) Δ E VP( G 3) SQED = 〈 Pa | U el VP | Pa 〉〈 PaPb | I $^{′′}$(Δ) | QaQb 〉 ( 〈 Qb | T$_{0}$ | Qb 〉 − 〈 Pb | T$_{0}$ | Pb 〉 ) , (64) Δ E VP( H ) SQED = 1 2 〈 PaPb | I $^{′}$(Δ) | QaQb 〉 ( 〈 Qb | U ml VP | Qb 〉 − 〈 Pb | U ml VP | Pb 〉 ) , (65) Δ E VP( I ) SQED = 1 2 〈 PaPb | I$_{VP}$ $^{′}$(Δ) | QaQb 〉 ( 〈 Qb | T$_{0}$ | Qb 〉 − 〈 Pb | T$_{0}$ | Pb 〉 ) . (66) 15