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Tensors and Relativity: Chapter 3

Tensors of type 2/0

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Recall that a vector can be regarded as a 1/0 tensor [ i.e. a map of one- forms into the reals ]. Therefore the outer product of two vectors defines a 2/0 tensor, i.e. it is a linear map from two one- forms to the reals:

equation1457

It follows that the most general 2/0 tensor is a linear sum of such outer products:

equation1467

where

equation1469

Under a Lorentz transformation, the components of f are:

equation1471

As before we can separate f into symmetric and anti- symmetric parts:

equation1476

and

equation1478


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