FCLoopCreateRulesToGLI
FCLoopCreateRulesToGLI[topo]
creates replacement rules for converting numerators from the given topology to GLI objects with inverse propagators.
It is also possible to use FCLoopCreateRulesToGLI[{topo1, topo2, ...}]
.
See also
Overview, FCTopology, GLI, FCLoopFindTopologies, FCLoopFindTopologyMappings.
Examples
1-loop tadpole
FCLoopCreateRulesToGLI[FCTopology[topo1, {SFAD[{p1, m^2}]}, {p1}, {}, {}, {}]]
{p12→Gtopo1(−1)+m2}
2-loop tadpole with 3 different masses
FCLoopCreateRulesToGLI[FCTopology[topo1, {SFAD[{p1, m1^2}], SFAD[{p2, m2^2}],
SFAD[{p1 - p2, m3^2}]}, {p1, p2}, {}, {}, {}]]
{p12→Gtopo1(−1,0,0)+m12,p22→Gtopo1(0,−1,0)+m22,p1⋅p2→21(Gtopo1(−1,0,0)+Gtopo1(0,−1,0)−Gtopo1(0,0,−1)+m12+m22−m32)}
2-loop self-energy
FCLoopCreateRulesToGLI[FCTopology["prop2Lv1",
{SFAD[{p1, m1^2}], SFAD[{p2, m2^2}], SFAD[p1 - q], SFAD[p2 - q],
SFAD[{p1 - p2, m3^2}]}, {p1, p2}, {Q}, {}, {}]]
{p12→Gprop2Lv1(−1,0,0,0,0)+m12,p22→Gprop2Lv1(0,−1,0,0,0)+m22,p1⋅p2→21(Gprop2Lv1(−1,0,0,0,0)+Gprop2Lv1(0,−1,0,0,0)−Gprop2Lv1(0,0,0,0,−1)+m12+m22−m32),p1⋅q→21(Gprop2Lv1(−1,0,0,0,0)−Gprop2Lv1(0,0,−1,0,0)+m12+q2),p2⋅q→21(Gprop2Lv1(0,−1,0,0,0)−Gprop2Lv1(0,0,0,−1,0)+m22+q2)}
A list of 3-loop self-energy topologies
topoList = {
FCTopology["prop3Lv1", {SFAD[p1], SFAD[p2], SFAD[p3], SFAD[p1 - p2], SFAD[p2 - p3], SFAD[p1 + q1],
SFAD[p2 + q1], SFAD[p3 + q1], SFAD[{{0, p1 . p3}}]}, {p1, p2, p3}, {q1}, {}, {}],
FCTopology["prop3L2", {SFAD[p1], SFAD[p2], SFAD[p3], SFAD[p1 - p2], SFAD[p2 - p3], SFAD[p1 - p3],
SFAD[p1 + q1], SFAD[p3 + q1], SFAD[{{0, (p1 - p2) . q1}}]}, {p1, p2, p3}, {q1}, {}, {}],
FCTopology["prop3L3", {SFAD[p1], SFAD[p1 - p4], SFAD[p3], SFAD[p4], SFAD[p1 - p3 - p4], SFAD[p1 + q1],
SFAD[p3 + p4 + q1], SFAD[p3 + q1], SFAD[{{0, (p4) . q1}}]}, {p1, p3, p4}, {q1}, {}, {}]
}
{FCTopology(prop3Lv1,{(p12+iη)1,(p22+iη)1,(p32+iη)1,((p1−p2)2+iη)1,((p2−p3)2+iη)1,((p1+q1)2+iη)1,((p2+q1)2+iη)1,((p3+q1)2+iη)1,(p1⋅p3+iη)1},{p1,p2,p3},{q1},{},{}),FCTopology(prop3L2,{(p12+iη)1,(p22+iη)1,(p32+iη)1,((p1−p2)2+iη)1,((p2−p3)2+iη)1,((p1−p3)2+iη)1,((p1+q1)2+iη)1,((p3+q1)2+iη)1,((p1−p2)⋅q1+iη)1},{p1,p2,p3},{q1},{},{}),FCTopology(prop3L3,{(p12+iη)1,((p1−p4)2+iη)1,(p32+iη)1,(p42+iη)1,((p1−p3−p4)2+iη)1,((p1+q1)2+iη)1,((p3+p4+q1)2+iη)1,((p3+q1)2+iη)1,(p4⋅q1+iη)1},{p1,p3,p4},{q1},{},{})}
FCLoopCreateRulesToGLI[topoList]
{{p12→Gprop3Lv1(−1,0,0,0,0,0,0,0,0),p22→Gprop3Lv1(0,−1,0,0,0,0,0,0,0),p32→Gprop3Lv1(0,0,−1,0,0,0,0,0,0),p1⋅p2→21(Gprop3Lv1(−1,0,0,0,0,0,0,0,0)+Gprop3Lv1(0,−1,0,0,0,0,0,0,0)−Gprop3Lv1(0,0,0,−1,0,0,0,0,0)),p1⋅p3→Gprop3Lv1(0,0,0,0,0,0,0,0,−1),p2⋅p3→21(Gprop3Lv1(0,−1,0,0,0,0,0,0,0)+Gprop3Lv1(0,0,−1,0,0,0,0,0,0)−Gprop3Lv1(0,0,0,0,−1,0,0,0,0)),p1⋅q1→21(−Gprop3Lv1(−1,0,0,0,0,0,0,0,0)+Gprop3Lv1(0,0,0,0,0,−1,0,0,0)−q12),p2⋅q1→21(−Gprop3Lv1(0,−1,0,0,0,0,0,0,0)+Gprop3Lv1(0,0,0,0,0,0,−1,0,0)−q12),p3⋅q1→21(−Gprop3Lv1(0,0,−1,0,0,0,0,0,0)+Gprop3Lv1(0,0,0,0,0,0,0,−1,0)−q12)},{p12→Gprop3L2(−1,0,0,0,0,0,0,0,0),p22→Gprop3L2(0,−1,0,0,0,0,0,0,0),p32→Gprop3L2(0,0,−1,0,0,0,0,0,0),p1⋅p2→21(Gprop3L2(−1,0,0,0,0,0,0,0,0)+Gprop3L2(0,−1,0,0,0,0,0,0,0)−Gprop3L2(0,0,0,−1,0,0,0,0,0)),p1⋅p3→21(Gprop3L2(−1,0,0,0,0,0,0,0,0)+Gprop3L2(0,0,−1,0,0,0,0,0,0)−Gprop3L2(0,0,0,0,0,−1,0,0,0)),p2⋅p3→21(Gprop3L2(0,−1,0,0,0,0,0,0,0)+Gprop3L2(0,0,−1,0,0,0,0,0,0)−Gprop3L2(0,0,0,0,−1,0,0,0,0)),p1⋅q1→21(−Gprop3L2(−1,0,0,0,0,0,0,0,0)+Gprop3L2(0,0,0,0,0,0,−1,0,0)−q12),p2⋅q1→21(−Gprop3L2(−1,0,0,0,0,0,0,0,0)+Gprop3L2(0,0,0,0,0,0,−1,0,0)−2Gprop3L2(0,0,0,0,0,0,0,0,−1)−q12),p3⋅q1→21(−Gprop3L2(0,0,−1,0,0,0,0,0,0)+Gprop3L2(0,0,0,0,0,0,0,−1,0)−q12)},{p12→Gprop3L3(−1,0,0,0,0,0,0,0,0),p32→Gprop3L3(0,0,−1,0,0,0,0,0,0),p42→Gprop3L3(0,0,0,−1,0,0,0,0,0),p1⋅p3→21(Gprop3L3(0,−1,0,0,0,0,0,0,0)+Gprop3L3(0,0,−1,0,0,0,0,0,0)−Gprop3L3(0,0,0,−1,0,0,0,0,0)−Gprop3L3(0,0,0,0,−1,0,0,0,0)+Gprop3L3(0,0,0,0,0,0,−1,0,0)−Gprop3L3(0,0,0,0,0,0,0,−1,0)−2Gprop3L3(0,0,0,0,0,0,0,0,−1)),p1⋅p4→21(Gprop3L3(−1,0,0,0,0,0,0,0,0)−Gprop3L3(0,−1,0,0,0,0,0,0,0)+Gprop3L3(0,0,0,−1,0,0,0,0,0)),p3⋅p4→21(−Gprop3L3(0,0,0,−1,0,0,0,0,0)+Gprop3L3(0,0,0,0,0,0,−1,0,0)−Gprop3L3(0,0,0,0,0,0,0,−1,0)−2Gprop3L3(0,0,0,0,0,0,0,0,−1)),p1⋅q1→21(−Gprop3L3(−1,0,0,0,0,0,0,0,0)+Gprop3L3(0,0,0,0,0,−1,0,0,0)−q12),p3⋅q1→21(−Gprop3L3(0,0,−1,0,0,0,0,0,0)+Gprop3L3(0,0,0,0,0,0,0,−1,0)−q12),p4⋅q1→Gprop3L3(0,0,0,0,0,0,0,0,−1)}}