FeynCalc manual (development version)

UnDeclareCommutator

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

See also

Overview, FCCommutator, CommutatorExplicit, DeclareNonCommutative, DotSimplify.

Examples

FCCommutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A], QuantumField[A]] = 0;

QuantumField[A] . QuantumField[A] . LeftPartialD[\[Nu]] . QuantumField[A] . QuantumField[A] . LeftPartialD[\[Nu]] 
 
ExpandPartialD[%]

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

6 A.A.\left(\partial _{\nu }A\right).\left(\partial _{\nu }A\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.\overleftarrow{\partial }_{\nu }.A.A.\overleftarrow{\partial }_{\nu }

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