Bug in FermionLineExpand@DiracMatrix with uncontracted momenta
In some cases, there is a bug if FermionLineExpand
is applied to a DiracMatrix
with uncontracted momenta, for example
expr1 = FermionLineExpand@DiracMatrix[LTensor[DiracG, \[Mu]1], DiracPL, Dirac1*mm + LTensor[DiracG, \[Alpha]]*LTensor[k1, \[Alpha]],
LTensor[DiracG, \[Mu]], LTensor[DiracG, \[Beta]], LTensor[DiracG, \[Nu]],
Dirac1*mm + LTensor[DiracG, \[Delta]]*LTensor[k1, \[Delta]], LTensor[DiracG, \[Mu]1], DiracPL]*LTensor[q2, \[Beta]];
expr2 = FermionLineExpand@DiracMatrix[LTensor[DiracG, \[Mu]1], DiracPL, Dirac1*mm + LTensor[DiracG, \[Alpha]]*LTensor[k1, \[Alpha]],
LTensor[DiracG, \[Mu]], Dirac1*mm*\[Kappa] + LTensor[DiracG, \[Beta]]*LTensor[q2, \[Beta]], LTensor[DiracG, \[Nu]],
Dirac1*mm + LTensor[DiracG, \[Delta]]*LTensor[k1, \[Delta]], LTensor[DiracG, \[Mu]1], DiracPL]/. \[Kappa] -> 0;
expr1 - expr2 //Simplify
should be zero, but it is not. In this case one should always use FermionLineExpand[...,DiracAlgebra->False]
first.