LeviCivita[mu, nu, rho, si] is an input function for the
totally antisymmetric Levi-Civita tensor. It evaluates automatically to
the internal representation
Eps[LorentzIndex[mu], LorentzIndex[nu], LorentzIndex[rho], LorentzIndex[si]]
(or with a second argument in LorentzIndex for the
Dimension, if the option Dimension of
LeviCivita is changed).
LeviCivita[mu , nu, ...][p, ...] evaluates to
Eps[LorentzIndex[mu], LorentzIndex[nu], ..., Momentum[p], ...].
The shortcut LeviCivita is deprecated, please use
LC instead!
LeviCivita[\[Alpha], \[Beta], \[Gamma], \[Delta]]\bar{\epsilon }^{\alpha \beta \gamma \delta }
LeviCivita[][p, q, r, s]\bar{\epsilon }^{\overline{p}\overline{q}\overline{r}\overline{s}}
LeviCivita[\[Alpha], \[Beta]][p, q]\bar{\epsilon }^{\alpha \beta \overline{p}\overline{q}}
LeviCivita[\[Alpha], \[Beta]][p, q] // StandardForm
(*Eps[LorentzIndex[\[Alpha]], LorentzIndex[\[Beta]], Momentum[p], Momentum[q]]*)LeviCivita is scheduled for removal in the future
versions of FeynCalc. The safe alternative is to use
LC.
LC[\[Alpha], \[Beta], \[Gamma], \[Delta]]\bar{\epsilon }^{\alpha \beta \gamma \delta }
LC[][p, q, r, s]\bar{\epsilon }^{\overline{p}\overline{q}\overline{r}\overline{s}}
LC[\[Alpha], \[Beta]][p, q]\bar{\epsilon }^{\alpha \beta \overline{p}\overline{q}}
LCD[\[Alpha], \[Beta], \[Gamma], \[Delta]]\overset{\text{}}{\epsilon }^{\alpha \beta \gamma \delta }
LCD[][p, q, r, s]\overset{\text{}}{\epsilon }^{pqrs}
LCD[\[Alpha], \[Beta]][p, q]\overset{\text{}}{\epsilon }^{\alpha \beta pq}
FCI[LC[\[Alpha], \[Beta], \[Gamma], \[Delta]]] === LeviCivita[\[Alpha], \[Beta], \[Gamma], \[Delta]]\text{True}
FCI[LCD[\[Alpha], \[Beta], \[Gamma], \[Delta]]] === LeviCivita[\[Alpha], \[Beta], \[Gamma], \[Delta], Dimension -> D]\text{True}