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LeviCivitaE

LTensor[LeviCivitaE,μ,ν,ρ,ς] or εμ,ν,ρ,ς
represents the Levi-Civita antisymmetric symbol near 4 spacetime dimensions.

Details and OptionsDetails and Options

  • ε,,, can be entered in StandardForm using EscleviEsc.
  • The indices of LeviCivitaE are ordered automatically.
  • Four-vectors contracted into LeviCivitaE appear as indices set in braces {}.
  • The indices of LeviCivitaE are assumed to run over dimensions (naive implementation of dimensional regularization).

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

The Levi-Civita antisymmetric symbol:

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Contract an external vector into the Levi-Civita antisymmetric symbol:

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Interpretation:

The Levi-Civita symbol vanishes if any pair of indices are identical:

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Sums or differences of vectors contracted into the Levi-Civita symbol can be expanded with Contract:

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The following quantity vanishes:

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