46 2. THEORIES, LAGRANGIANS AND COUNTERTERMS
Figure 3. The renormalization group differential equation.
Next consider γ2, given by
Since there are no external edges there is no dependence on a ∈
and we find
wγ2 (P (ε, L),I) =
Kl1 (x, y)Kl2 (x, y)Kl3 (x, y)d VolM×M .
Using the fact that
+ higher order terms
for l small, we can see that the limit of wγ2 (P (ε, L),I) as ε → 0 is singular.
Let γ3 be the graph