FeynCalc manual (development version)

FCLoopBasisOverdeterminedQ

FCLoopBasisOverdeterminedQ[int, {q1, q2, ...}] checks whether the loop integral or topology int contains linearly dependent propagators.

The input can also consist of an FCTopology object or a list thereof.

See also

Overview, FCLoopBasisIncompleteQ.

Examples

FAD[{q1, m1}, {q1 - l + p, m}] 
 
FCLoopBasisOverdeterminedQ[%, {q1}]

\frac{1}{\left(\text{q1}^2-\text{m1}^2\right).\left((-l+p+\text{q1})^2-m^2\right)}

\text{False}

FAD[q1, {q1, m1}] 
 
FCLoopBasisOverdeterminedQ[%, {q1}]

\frac{1}{\text{q1}^2.\left(\text{q1}^2-\text{m1}^2\right)}

\text{True}

FAD[q1, q2, {q1 + l, m1}, {q1 - l, m1}, {q2 + l, m1}, {q2 - l, m1}] 
 
FCLoopBasisOverdeterminedQ[%, {q1, q2}]

\frac{1}{\text{q1}^2.\text{q2}^2.\left((l+\text{q1})^2-\text{m1}^2\right).\left((\text{q1}-l)^2-\text{m1}^2\right).\left((l+\text{q2})^2-\text{m1}^2\right).\left((\text{q2}-l)^2-\text{m1}^2\right)}

\text{True}

FCLoopBasisOverdeterminedQ[FCTopology[topo1, {FAD[p1], FAD[p2], 
    FAD[p1 - q], FAD[p2 - q], FAD[p1 - p2], FAD[p1 + p2 + q]}, {p1, p2}, {q}, {}, {}]]

\text{True}

FCLoopBasisOverdeterminedQ[{FCTopology[topo1, {FAD[p1], FAD[p2], 
     FAD[p1 - q], FAD[p2 - q], FAD[p1 - p2], FAD[p1 + p2 + q]}, {p1, p2}, {q}, {}, {}], 
   FCTopology[topo2, {FAD[p1], FAD[p2], 
     FAD[p1 - q], FAD[p2 - q], FAD[p1 - p2]}, {p1, p2}, {q}, {}, {}] 
  }]

\{\text{True},\text{False}\}