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Transverse

Transverse[tensor]
gives the transverse scalar projection of the rank-two tensor containing only one four-vector.

Transverse[tensor,v]
gives the scalar projection of the given rank-two tensor transverse to vector v.

Transverse[tensor,v,{μ,ν}]
gives the rank tensor projection of the rank tensor transverse 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 .
  • Transverse[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, Transverse attempts to determine them automatically.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

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

In[1]:=
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Out[1]=

Call LoopRefine to safely take and drop higher orders in ϵ:

In[2]:=
Click for copyable input
Out[2]=