LeviCivita

Description

LeviCivita[μ,  ν,  ρ,  σ] is an input function for the totally antisymmetric Levi-Civita tensor. It evaluates automatically to the internal representation Eps[ LorentzIndex[μ], LorentzIndex[ν], LorentzIndex[ρ], LorentzIndex[Cell[σ]] ] (or with a second argument in LorentzIndex for the Dimension, if the option Dimension of LeviCivita is changed). LeviCivita[μ,  ν  ... ][ p,   .. .] evaluates to Eps[LorentzIndex[μ], LorentzIndex[ν], ..., Momentum[p], ...].

Options[LeviCivita]

See also:  LC, LCD.

Examples

LeviCivita[α, β, γ, δ]

LeviCivita[μ, ν][OPEDelta, p]

LeviCivita[][p, q, r, s]

LeviCivita[α, β, β, δ]

LeviCivita[μ, ν][OPEDelta, p] // StandardForm

t1  =  
      LeviCivita[α, β, γ, ρ] . 
        LeviCivita[α, β, γ, ρ]

Contract[t1]

SetOptions[LeviCivita, Dimension -> D]; 
    SetOptions[Eps, Dimension -> D];

Contract[ 
        LeviCivita[α, β, γ, ρ] . 
          LeviCivita[α, β, γ, ρ]] // 
      Factor2

SetOptions[LeviCivita, Dimension -> 4]; 
    SetOptions[Eps, Dimension -> 4];

LC[α, β, γ, δ]

Clear[t1]