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gives the longitudinal scalar projection of the rank-two tensor containing only one four-vector.

gives the scalar projection of the given rank-two tensor longitudinal to vector v.

gives the rank tensor projection of the rank tensor longitudinal to vector v along indices μ and ν.

Details and OptionsDetails and Options

  • Given a four-vector and two indices , , a rank tensor can be generically be written .
  • Longitudinal[tensor] extracts the rank tensor by multiplying tensor with the projector and applying Contract.
  • If the four-vector v and indices μ, ν are not explicitly specified, Longitudinal attempts to determine them automatically.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Project the longitudinal part out of a simple rank-2 tensor:

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