MetricTensor[mu, nu] is the metric tensor. The default
dimension is 4.
The shortcut MetricTensor is deprecated, please use
MT instead!
MetricTensor[\[Alpha], \[Beta]]
Contract[% %]\bar{g}^{\alpha \beta }
4
MetricTensor[\[Alpha], \[Beta], Dimension -> D]
Contract[% %]g^{\alpha \beta }
D
StandardForm[MetricTensor[a, b]]
(*Pair[LorentzIndex[a], LorentzIndex[b]]*)MetricTensor is scheduled for removal in the future
versions of FeynCalc. The safe alternative is to use
MT.
MT[\[Mu], \[Nu]]\bar{g}^{\mu \nu }
MTD[\[Mu], \[Nu]]g^{\mu \nu }
FCI[MT[\[Mu], \[Nu]]] === MetricTensor[\[Mu], \[Nu]]
FCI[MTD[\[Mu], \[Nu]]] === MetricTensor[\[Mu], \[Nu], Dimension -> D]\text{True}
\text{True}