ChangeDimension

Description

ChangeDimension[exp, dim] changes all LorentzIndex and Momenta in exp to dimension dim (and also Levi-Civita-tensors, Dirac slashes and Dirac matrices).

See also:  LorentzIndex, Momentum, DiracGamma, Eps.

Examples

Remember that LorentzIndex[mu, 4] is simplified to LorentzIndex[mu] and Momentum[p, 4] to Momentum[p]. Thus the fullowing objects are defined in four dimensions.

{LorentzIndex[μ],  Momentum[p]}

ChangeDimension[%,  D]

% // StandardForm

This changes all non-4-dimensional objects to 4-dimensional ones.

ChangeDimension[%%,  4]  //  StandardForm

Consider the following list of 4- and D-dimensional object.

{GA[μ, ν] MT[μ, ν],  
      GAD[μ, ν] MTD[μ, ν] f[D]}

DiracTrick[Contract[%]]

DiracTrick[Contract[ChangeDimension[%%, n]]]

Any explicit occurence of D (like in f(D)) is not replaced by ChangeDimension.

SetOptions[LeviCivita, Dimension -> D];

The option Dimension of Eps must be changed too, since with the default setting Dimension->4 the arguments of Eps are automatically changed to 4 dimensions.

SetOptions[Eps, Dimension -> D];

a1  =  LeviCivita[μ, ν, ρ, σ]

a2  =  ChangeDimension[a1, 4]

Factor2[Contract[(a1^2)]]

Contract[(a2^2)]

SetOptions[Eps, Dimension -> 4];

Clear[a1, a2];