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]}
ex = ChangeDimension[%, D]\left\{\mu ,\overline{p}\right\}
\{\mu ,p\}
ex // StandardForm
(*{LorentzIndex[\[Mu], D], Momentum[p, D]}*)This changes all non-4-dimensional objects to 4-dimensional ones
ChangeDimension[%%, 4] // StandardForm
(*{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]}
DiracTrick /@ Contract /@ %
DiracTrick /@ Contract /@ ChangeDimension[%%, n]\left\{\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu } \bar{g}^{\mu \nu },f(D) \gamma ^{\mu }.\gamma ^{\nu } g^{\mu \nu }\right\}
\{4,D f(D)\}
\{n,n f(D)\}
Any explicit occurrence of D (like in f(D)) is not replaced by ChangeDimension.
LC[\[Mu], \[Nu], \[Rho], \[Sigma]]
ChangeDimension[%, D]
Factor2[Contract[%^2]]\bar{\epsilon }^{\mu \nu \rho \sigma }
\overset{\text{}}{\epsilon }^{\mu \nu \rho \sigma }
(1-D) (2-D) (3-D) D
Contract[LC[\[Mu], \[Nu], \[Rho], \[Sigma]]^2]-24