Derive (23) from first principles, that is from (11). You should find a symmetry factor 1/2. 5

Derive (23) from first principles, that is from (11). You should find a symmetry factor 1/2.

  

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5 k₁ Figure 1.7.10 KA i i 2 (-ix)² / (27/² k²_m² + i= (k₂ + k₂ − k)² —, k₁+k₂-k 14₂ 1.7. Feynman Diagrams | 57 Loops and a first look at divergence Just as in our baby problem, we have tree diagrams and loop diagrams. So far we have only looked at tree diagrams. Our next example is the loop diagram in figure 1.7.10 (compare fig. 1.7.2a.) Applying the Feynman rules, we obtain You should now be ready for field theory! Indeed, the functional integral in (1) (which I repeat here) Z(J) =D¹²²²²-02/45p+pl (23) (11) 5 k₁ Figure 1.7.10 KA i i 2 (-ix)² / (27/² k²_m² + i= (k₂ + k₂ − k)² —, k₁+k₂-k 14₂ 1.7. Feynman Diagrams | 57 Loops and a first look at divergence Just as in our baby problem, we have tree diagrams and loop diagrams. So far we have only looked at tree diagrams. Our next example is the loop diagram in figure 1.7.10 (compare fig. 1.7.2a.) Applying the Feynman rules, we obtain You should now be ready for field theory! Indeed, the functional integral in (1) (which I repeat here) Z(J) =D¹²²²²-02/45p+pl (23) (11)

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