DiracOrder[exp]
orders the Dirac matrices in exp
lexicographically. DiracOrder[exp, orderlist]
orders the Dirac matrices in exp
according to orderlist
. DiracOrder
is also an option of DiracSimplify
and some other functions dealing with Dirac algebra. If set to True
, the function DiracOrder
will be applied to the intermediate result to reorder the Dirac matrices lexicographically.
Overview, DiracSimplify, DiracTrick.
[\[Beta], \[Alpha]]
GA
[%] DiracOrder
DiracOrder
also works with Dirac matrices in -dimensions.
[\[Rho], \[Nu], \[Mu], \[Nu]]
GAD
[%] DiracOrder
By default is moved to the right.
[5, \[Mu], \[Nu]]
GA
[%] DiracOrder
[6, \[Mu], 7]
GA
[%] DiracOrder
orderlist
comes into play when we need an ordering that is not lexicographic
[\[Alpha], \[Beta], \[Delta]]
GA
[%] DiracOrder
[GA[\[Alpha], \[Beta], \[Delta]], {\[Delta], \[Beta], \[Alpha]}] DiracOrder
Reordering of Dirac matrices in long chains is expensive, so that DiracSimplify
does not do it by default.
[GAD[\[Mu], \[Nu]] + GAD[\[Nu], \[Mu]]] DiracSimplify
However, if you know that it can lead to simpler expressions, you can activate the reordering via the option DiracOrder
.
[GAD[\[Mu], \[Nu]] + GAD[\[Nu], \[Mu]], DiracOrder -> True] DiracSimplify
Reproduce Eq. 18.128 from An Introduction to Quantum Field Theory by M. Peskin and D. Schroeder.
[1/2 (GAD[\[Mu], \[Alpha], \[Nu]] + GAD[\[Nu], \[Alpha], \[Mu]]), DiracOrder -> True] DiracSimplify