Identities for topologies with insertions Sample Clauses

Identities for topologies with insertions. When a topology contains a line that does not have an integer power, the method of the previous section has to be slightly extended. Such cases occur either when the input diagram(s) can be written with a higher-order propagator in it, or when during the reduction a two-point function can be integrated out. If the resulting topology needs a custom reduction, we not only have to lower powers of denominators and numerators, but we also have to bring the powers of the non-integer lines to a canonical value, which we take to be 1 + me for some positive integer m. As an example, we consider the two-loop t1star05 topology (see also refs. [32, 33]) p1 p2
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