FeynCalc manual (development version)

FCLoopFindIncompleteTopologies

FCLoopFindOverdeterminedTopologies[topos] finds topologies with incomplete propagator bases in the given list of topologies. The function returns a list of two lists, where the first list contains all incomplete topologies and the second one the rest.

See also

Overview, FCTopology, FCLoopFindIncompleteTopologies, FCLoopFindTopologies, FCLoopFindTopologyMappings, SubtopologyMarker.

Examples

topos = {FCTopology[topo1, {SFAD[k1], SFAD[k1 + p], SFAD[k1 - p]}, {k1}, {p}, {}, {}], 
   FCTopology[topo2, {SFAD[k1], SFAD[k1 + p]}, {k1}, {p}, {}, {}], 
   FCTopology[topo3, {SFAD[k1], SFAD[k2]}, {k1, k2}, {}, {}, {}]}

\left\{\text{FCTopology}\left(\text{topo1},\left\{\frac{1}{(\text{k1}^2+i \eta )},\frac{1}{((\text{k1}+p)^2+i \eta )},\frac{1}{((\text{k1}-p)^2+i \eta )}\right\},\{\text{k1}\},\{p\},\{\},\{\}\right),\text{FCTopology}\left(\text{topo2},\left\{\frac{1}{(\text{k1}^2+i \eta )},\frac{1}{((\text{k1}+p)^2+i \eta )}\right\},\{\text{k1}\},\{p\},\{\},\{\}\right),\text{FCTopology}\left(\text{topo3},\left\{\frac{1}{(\text{k1}^2+i \eta )},\frac{1}{(\text{k2}^2+i \eta )}\right\},\{\text{k1},\text{k2}\},\{\},\{\},\{\}\right)\right\}

FCLoopFindIncompleteTopologies[topos]

\left\{\left\{\text{FCTopology}\left(\text{topo3},\left\{\frac{1}{(\text{k1}^2+i \eta )},\frac{1}{(\text{k2}^2+i \eta )}\right\},\{\text{k1},\text{k2}\},\{\},\{\},\{\}\right)\right\},\left\{\text{FCTopology}\left(\text{topo1},\left\{\frac{1}{(\text{k1}^2+i \eta )},\frac{1}{((\text{k1}+p)^2+i \eta )},\frac{1}{((\text{k1}-p)^2+i \eta )}\right\},\{\text{k1}\},\{p\},\{\},\{\}\right),\text{FCTopology}\left(\text{topo2},\left\{\frac{1}{(\text{k1}^2+i \eta )},\frac{1}{((\text{k1}+p)^2+i \eta )}\right\},\{\text{k1}\},\{p\},\{\},\{\}\right)\right\}\right\}