FeynCalc manual (development version)

TIDL

TIDL is a database of tensorial reduction formulas.

See also

Overview, TID.

Examples

TIDL[{q, mu}, {p}]

pmu(pq)p2\frac{p^{\text{mu}} (p\cdot q)}{p^2}

TIDL[{q, mu}, {p1, p2}]

p1mu((p1  p2)(p2q)p22(p1q))(p1  p2)2p12  p22p2mu(p12(p2q)(p1  p2)(p1q))(p1  p2)2p12  p22\frac{\text{p1}^{\text{mu}} \left((\text{p1}\cdot \;\text{p2}) (\text{p2}\cdot q)-\text{p2}^2 (\text{p1}\cdot q)\right)}{(\text{p1}\cdot \;\text{p2})^2-\text{p1}^2 \;\text{p2}^2}-\frac{\text{p2}^{\text{mu}} \left(\text{p1}^2 (\text{p2}\cdot q)-(\text{p1}\cdot \;\text{p2}) (\text{p1}\cdot q)\right)}{(\text{p1}\cdot \;\text{p2})^2-\text{p1}^2 \;\text{p2}^2}

TIDL[{{q1, mu}, {q2, nu}}, {p}]

gmu  nu((p  q1)(p  q2)p2(q1  q2))(1D)p2pmupnu(D(p  q1)(p  q2)p2(q1  q2))(1D)p4\frac{g^{\text{mu}\;\text{nu}} \left((p\cdot \;\text{q1}) (p\cdot \;\text{q2})-p^2 (\text{q1}\cdot \;\text{q2})\right)}{(1-D) p^2}-\frac{p^{\text{mu}} p^{\text{nu}} \left(D (p\cdot \;\text{q1}) (p\cdot \;\text{q2})-p^2 (\text{q1}\cdot \;\text{q2})\right)}{(1-D) p^4}

TIDL[{{q1, mu}, {q2, nu}}, {}]

gmu  nu(q1  q2)D\frac{g^{\text{mu}\;\text{nu}} (\text{q1}\cdot \;\text{q2})}{D}