Eps

Description

Eps[a, b, c, d] is the head of the totally antisymmetric  ϵ (Levi-Civita) tensor. The a,b, ... may have head LorentzIndex, Momentum or Integer. In case of integers the Levi-Civita tensor is evaluated immediately.

Options[Eps]

See also:  EpsEvaluate, LC, LCD, LeviCivita.

Examples

Eps[LorentzIndex[μ], LorentzIndex[ν], LorentzIndex[ρ], 
      LorentzIndex[σ]]

Eps[Momentum[p], LorentzIndex[ν], LorentzIndex[ρ], 
      LorentzIndex[σ]]

Eps[b, a, c, d] // StandardForm

Eps[0, 1, 2, 3]

Eps[1, 0, 2, 3]

SetOptions[Eps, Dimension -> 4];

a1  = 
      Eps[LorentzIndex[μ, D], LorentzIndex[ν, D], 
        LorentzIndex[ρ, D], LorentzIndex[σ, D]]

Contract[a1  a1]

SetOptions[Eps, Dimension -> D];

a2  = 
      Eps[LorentzIndex[μ, D], LorentzIndex[ν, D], 
        LorentzIndex[ρ, D], LorentzIndex[σ, D]]

Contract[a2  a2] // Factor2

g5 = -(I/24) LCD[μ, ν, ρ, α] . 
            GAD[μ, ν, ρ, α] // FCI

g5p=-(I/24) LCD[μ',ν',ρ',α'].GAD[μ',ν',ρ',α']//FCI

g52 = Factor2[Calc[g5 . g5p]]

g52 /. D -> 4

Clear[a1, a2, g5, g5p, g52]