Δ E SE( H 1) SQED = i 2 π ∫ d ω ∑ n 1 , 2 〈 Pan$_{2}$ | I ( ω ) | n$_{1}$Pa 〉〈 n$_{1}$ | T$_{0}$ | n$_{2}$ 〉 ( ε$_{Pa}$ − ω − uε$_{n}$$_{1}$ )( ε$_{Pa}$ − ω − uε$_{n}$$_{2}$ ) 〈 PaPb | I $^{′}$(Δ) | QaQb 〉 , (36) Δ E SE( H 2) SQED = i 2 π ∫ d ω ∑ n 1 , 2 〈 Pan$_{2}$ | I ( ω ) | n$_{1}$Qa 〉〈 n$_{1}$Pb | I $^{′}$(Δ) | n$_{2}$Qb 〉 ( ε$_{Pa}$ − ω − uε$_{n}$$_{1}$ )( ε$_{Qa}$ − ω − uε$_{n}$$_{2}$ ) × ( 〈 Qb | T$_{0}$ | Qb 〉 − 〈 Pb | T$_{0}$ | Pb 〉 ) , (37) Δ E SE( H 3) SQED = 2 ∑ n 1 ′ 1 ε$_{Pa}$ − ε$_{n}$$_{1}$ [ 〈 Pa | Σ $^{′}$( ε$_{Pa}$ ) | n$_{1}$ 〉〈 n$_{1}$ | T$_{0}$ | Pa 〉〈 PaPb | I (Δ) | QaQb 〉 + 〈 Pa | Σ $^{′}$( ε$_{Pa}$ ) | n$_{1}$ 〉〈 n$_{1}$Pb | I (Δ) | QaQb 〉〈 Pa | T$_{0}$ | Pa 〉 ] + 〈 Pa | Σ $^{′}$( ε$_{Pa}$ ) | Pa 〉 { 2 ∑ n 1 ′ [ 〈 Pa | T$_{0}$ | n$_{1}$ 〉〈 n$_{1}$Pb | I (Δ) | QaQb 〉 ε$_{Pa}$ − ε$_{n}$$_{1}$ + 〈 Pb | T$_{0}$ | n$_{1}$ 〉〈 Pan$_{1}$ | I (Δ) | QaQb 〉 ε$_{Pb}$ − ε$_{n}$$_{1}$ ] + 〈 PaPb | I $^{′}$(Δ) | QaQb 〉 ( 〈 Pa | T$_{0}$ | Pa 〉 + 〈 Qb | T$_{0}$ | Qb 〉 − 〈 Pb | T$_{0}$ | Pb 〉 ) } . (38) Δ E SE( C 1) SQED (UV) = 2 L (1) ∑ n 1 ′ 〈 Pa | T$_{0}$ | n$_{1}$ 〉〈 n$_{1}$Pb | I (Δ) | QaQb 〉 ε$_{Pa}$ − ε$_{n}$$_{1}$ , (39) Δ E SE( C 2) SQED (UV) = 2 L (1) ∑ n 1 ′ 〈 PaPb | I (Δ) | n$_{1}$Qb 〉〈 n$_{1}$ | T$_{0}$ | Qa 〉 ε$_{Qa}$ − ε$_{n}$$_{1}$ , (40) Δ E SE( F ) $_{SQED}$(UV) = 2 L (1) ∑ n 1 ′ 〈 PaPb | I (Δ) | Qan$_{1}$ 〉〈 n$_{1}$ | T$_{0}$ | Qb 〉 ε$_{Qb}$ − ε$_{n}$$_{1}$ , (41) Δ E SE( H 1) SQED (UV) = L (1) 〈 Pa | T$_{0}$ | Pa 〉〈 PaPb | I $^{′}$(Δ) | QaQb 〉 , (42) Δ E SE( H 2) SQED (UV) = L (1) 〈 PaPb | I $^{′}$(Δ) | QaQb 〉 ( 〈 Qb | T$_{0}$ | Qb 〉 − 〈 Pb | T$_{0}$ | Pb 〉 ) , (43) Δ E SE( H 3) SQED (UV) = 2 B (1) ∑ n 1 ′ ( 〈 Pa | T$_{0}$ | n$_{1}$ 〉〈 n$_{1}$Pb | I (Δ) | QaQb 〉 ε$_{Pa}$ − ε$_{n}$$_{1}$ + 〈 Pb | T$_{0}$ | n$_{1}$ 〉〈 Pan$_{1}$ | I (Δ) | QaQb 〉 ε$_{Pb}$ − ε$_{n}$$_{1}$ ) + B (1) 〈 PaPb | I $^{′}$(Δ) | QaQb 〉 ( 〈 Pa | T$_{0}$ | Pa 〉 + 〈 Qb | T$_{0}$ | Qb 〉 − 〈 Pb | T$_{0}$ | Pb 〉 . (44) 10 Equations (31)–(38) diverge both in ultraviolet and infrar ed regions. The UV-divergent terms are: