FeynCalc manual (development version)

UnDeclareCommutator

UnDeclareCommutator[a, b] undeclares the value assigned to the commutator of a and b.

See also

Overview, Commutator, CommutatorExplicit, DeclareNonCommutative, DotSimplify.

Examples

Commutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A], QuantumField[A]] = 0;
QuantumField[A] . QuantumField[A] . LeftPartialD[\[Nu]] . QuantumField[A] . QuantumField[A] . LeftPartialD[\[Nu]] 
 
ExpandPartialD[%]

A.A.ν.A.A.νA.A.\overleftarrow{\partial }_{\nu }.A.A.\overleftarrow{\partial }_{\nu }

6A.A.((νA)).((νA))+A.(ννA).A.A+(ννA).A.A.A6 A.A.\left(\left.(\partial _{\nu }A\right)\right).\left(\left.(\partial _{\nu }A\right)\right)+A.\left(\partial _{\nu }\partial _{\nu }A\right).A.A+\left(\partial _{\nu }\partial _{\nu }A\right).A.A.A

UnDeclareCommutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A], QuantumField[A]];
QuantumField[A] . QuantumField[A] . LeftPartialD[\[Nu]] . QuantumField[A] . QuantumField[A] . LeftPartialD[\[Nu]] 
 
ExpandPartialD[%]

A.A.ν.A.A.νA.A.\overleftarrow{\partial }_{\nu }.A.A.\overleftarrow{\partial }_{\nu }

A.((νA)).A.((νA))+A.((νA)).((νA)).A+((νA)).A.A.((νA))+((νA)).A.((νA)).A+2((νA)).((νA)).A.A+A.(ννA).A.A+(ννA).A.A.AA.\left(\left.(\partial _{\nu }A\right)\right).A.\left(\left.(\partial _{\nu }A\right)\right)+A.\left(\left.(\partial _{\nu }A\right)\right).\left(\left.(\partial _{\nu }A\right)\right).A+\left(\left.(\partial _{\nu }A\right)\right).A.A.\left(\left.(\partial _{\nu }A\right)\right)+\left(\left.(\partial _{\nu }A\right)\right).A.\left(\left.(\partial _{\nu }A\right)\right).A+2 \left(\left.(\partial _{\nu }A\right)\right).\left(\left.(\partial _{\nu }A\right)\right).A.A+A.\left(\partial _{\nu }\partial _{\nu }A\right).A.A+\left(\partial _{\nu }\partial _{\nu }A\right).A.A.A