FCLoopCreateRuleGLIToGLI[topology1, topology2] creates a GLI replacement rule assuming that the topology2 is a subtopology of topology1. Both topologies must be given as FCTopology objects.
It is also possible to use FCLoopCreateRuleGLIToGLI[topo1, {subtopo1, subtopo2, ...}] provided that {subtopo1, subtopo2, ...} are subtopologies of topo1 that were obtained by removing some propagators from topo1 and not performing any loop momentum shifts afterwards.
Furthermore, when working with lists of topologies one can write FCLoopCreateRuleGLIToGLI[{topo1, topo2, ...}, {{subtopo11, subtopo12, ...}, {subtopo21, subtopo22, ...}, ..}].
Overview, FCTopology, GLI, FCLoopFindTopologies, FCLoopFindTopologyMappings.
FCLoopCreateRuleGLIToGLI[FCTopology[topo1, {SFAD[p]}], FCTopology[topo2, {SFAD[p]}]]G^{\text{topo2}}(\text{n1$\_$}):\to G^{\text{topo1}}(\text{n1})
FCLoopCreateRuleGLIToGLI[FCTopology[topo1, {SFAD[p], SFAD[q]}],
FCTopology[topo2, {SFAD[p]}]]G^{\text{topo2}}(\text{n1$\_$}):\to G^{\text{topo1}}(\text{n1},0)
FCLoopCreateRuleGLIToGLI[FCTopology[topo1, {SFAD[p], SFAD[q]}],
FCTopology[topo2, {SFAD[q], SFAD[p]}]]G^{\text{topo2}}(\text{n2$\_$},\text{n1$\_$}):\to G^{\text{topo1}}(\text{n1},\text{n2})
FCLoopCreateRuleGLIToGLI[FCTopology[topo1, {SFAD[r], SFAD[p], SFAD[q]}],
FCTopology[topo2, {SFAD[p]}]]G^{\text{topo2}}(\text{n2$\_$}):\to G^{\text{topo1}}(0,\text{n2},0)
FCLoopCreateRuleGLIToGLI[FCTopology["tmpTopo4",
{SFAD[{{0, (k1 + k2) . nb}, {0, 1}, 1}], SFAD[{{0, (k1 - k3) . n}, {0, 1}, 1}],
SFAD[{{0, n . (-k1 - k2 + q)}, {0, 1}, 1}], SFAD[{{0, nb . (-k1 + k3 + q)}, {0, 1}, 1}],
SFAD[{{-k1, 0}, {0, 1}, 1}], SFAD[{{k2, 0}, {0, 1}, 1}], SFAD[{{k1 + k2, 0}, {0, 1}, 1}],
SFAD[{{-k3, 0}, {0, 1}, 1}], SFAD[{{-k1 + k3, 0}, {0, 1}, 1}],
SFAD[{{k1 - k3 - q, 0}, {0, 1}, 1}], SFAD[{{k1 + k2 - k3 - q, 0}, {0, 1}, 1}],
SFAD[{{-k1 - k2 + q, 0}, {0, 1}, 1}]}],
FCTopology["tmpTopo18", {SFAD[{{0, (k1 + k2) . nb}, {0, 1}, 1}],
SFAD[{{0, n . (-k1 - k2 + q)}, {0, 1}, 1}], SFAD[{{0, nb . (-k1 + k3 + q)}, {0, 1}, 1}],
SFAD[{{-k1, 0}, {0, 1}, 1}], SFAD[{{k2, 0}, {0, 1}, 1}],
SFAD[{{k1 + k2, 0}, {0, 1}, 1}], SFAD[{{-k3, 0}, {0, 1}, 1}],
SFAD[{{-k1 + k3, 0}, {0, 1}, 1}], SFAD[{{k1 - k3 - q, 0}, {0, 1}, 1}],
SFAD[{{k1 + k2 - k3 - q, 0}, {0, 1}, 1}], SFAD[{{-k1 - k2 + q, 0}, {0, 1}, 1}]}]]G^{\text{tmpTopo18}}(\text{n1$\_$},\text{n3$\_$},\text{n4$\_$},\text{n5$\_$},\text{n6$\_$},\text{n7$\_$},\text{n8$\_$},\text{n9$\_$},\text{n10$\_$},\text{n11$\_$},\text{n12$\_$}):\to G^{\text{tmpTopo4}}(\text{n1},0,\text{n3},\text{n4},\text{n5},\text{n6},\text{n7},\text{n8},\text{n9},\text{n10},\text{n11},\text{n12})
FCLoopIntegralToGraph[FCTopology["tad2l", {FAD[{p1, m1}], FAD[{p2, m2}], FAD[{p1 - p2, m3}]},
{p1, p2}, {}, {}, {}]]\left\{\{1\to 2,1\to 2,1\to 2\},\left( \begin{array}{ccc} \;\text{p1} & 1 & -\text{m1}^2 \\ \;\text{p2} & 1 & -\text{m2}^2 \\ \;\text{p1}-\text{p2} & 1 & -\text{m3}^2 \\ \end{array} \right),\left\{\frac{1}{(\text{p1}^2-\text{m1}^2+i \eta )},\frac{1}{(\text{p2}^2-\text{m2}^2+i \eta )},\frac{1}{((\text{p1}-\text{p2})^2-\text{m3}^2+i \eta )}\right\},1\right\}
FCLoopCreateRuleGLIToGLI[
{FCTopology["prop2l", {FAD[{p1, m1}], FAD[{p2, m2}], FAD[{p1 - q, m3}], FAD[{p1 - q, m4}],
FAD[{p1 - p2, m5}]}, {p1, p2}, {q}, {}, {}],
FCTopology["tad2l", {FAD[{p1, m1}], FAD[{p2, m2}], FAD[{p1 - p2, m3}]}, {p1, p2}, {}, {}, {}]}, {
{
FCTopology["prop2lX1", {FAD[{p2, m2}], FAD[{p1 - q, m3}], FAD[{p1 - q, m4}], FAD[{p1 - p2, m5}]},
{p1, p2}, {q}, {}, {}],
FCTopology["prop2lX5", {FAD[{p1, m1}], FAD[{p2, m2}], FAD[{p1 - q, m3}], FAD[{p1 - q, m4}]},
{p1, p2}, {q}, {}, {}]
},
{
FCTopology["tad2lX2", {FAD[{p1, m1}], FAD[{p1 - p2, m3}]}, {p1, p2}, {}, {}, {}],
FCTopology["tad2lX3", {FAD[{p1, m1}], FAD[{p2, m2}]}, {p1, p2}, {}, {}, {}]
}
}]\left\{\left\{G^{\text{prop2lX1}}(\text{n2$\_$},\text{n3$\_$},\text{n4$\_$},\text{n5$\_$}):\to G^{\text{prop2l}}(0,\text{n2},\text{n3},\text{n4},\text{n5}),G^{\text{prop2lX5}}(\text{n1$\_$},\text{n2$\_$},\text{n3$\_$},\text{n4$\_$}):\to G^{\text{prop2l}}(\text{n1},\text{n2},\text{n3},\text{n4},0)\right\},\left\{G^{\text{tad2lX2}}(\text{n1$\_$},\text{n3$\_$}):\to G^{\text{tad2l}}(\text{n1},0,\text{n3}),G^{\text{tad2lX3}}(\text{n1$\_$},\text{n2$\_$}):\to G^{\text{tad2l}}(\text{n1},\text{n2},0)\right\}\right\}
Using the option Reverse we can also generate inverse replacement rules
FCLoopCreateRuleGLIToGLI[FCTopology[topo1, {SFAD[p], SFAD[q]}],
FCTopology[topo2, {SFAD[q], SFAD[p]}], Reverse -> True]G^{\text{topo1}}(\text{n1$\_$},\text{n2$\_$}):\to G^{\text{topo2}}(\text{n2},\text{n1})
FCLoopCreateRuleGLIToGLI[FCTopology[topo1, {SFAD[p], SFAD[q]}],
FCTopology[topo2, {SFAD[p]}]]G^{\text{topo2}}(\text{n1$\_$}):\to G^{\text{topo1}}(\text{n1},0)