ChangeDimension[exp, dim]
changes all LorentzIndex
and Momentum
symbols in exp
to dimension dim
(and also Levi-Civita-tensors, Dirac slashes and Dirac matrices).
Notice that the dimension of CartesianIndex
and CartesianMomentum
objects will be changed to dim-1
, not dim
.
Overview, LorentzIndex, Momentum, DiracGamma, Eps.
Remember that LorentzIndex[mu, 4]
is simplified to LorentzIndex[mu]
and Momentum[p, 4]
to Momentum[p]
. Thus the following objects are defined in four dimensions.
{LorentzIndex[\[Mu]], Momentum[p]}
= ChangeDimension[%, D] ex
// StandardForm
ex
(*{LorentzIndex[\[Mu], D], Momentum[p, D]}*)
This changes all non-4-dimensional objects to 4-dimensional ones
[%%, 4] // StandardForm
ChangeDimension
(*{LorentzIndex[\[Mu]], Momentum[p]}*)
Consider the following list of 4- and D-dimensional objects
{GA[\[Mu], \[Nu]] MT[\[Mu], \[Nu]], GAD[\[Mu], \[Nu]] MTD[\[Mu], \[Nu]] f[D]}
/@ Contract /@ %
DiracTrick
/@ Contract /@ ChangeDimension[%%, n] DiracTrick
Any explicit occurrence of (like in ) is not replaced by ChangeDimension
.
[\[Mu], \[Nu], \[Rho], \[Sigma]]
LC
[%, D]
ChangeDimension
[Contract[%^2]] Factor2
[LC[\[Mu], \[Nu], \[Rho], \[Sigma]]^2] Contract