Structure
The spacetime algebra is built up from combinations of one time-like basis vector and three orthogonal space-like vectors, under the multiplication rule
where is the Minkowski metric with signature (+ − − −)
Thus, otherwise .
The basis vectors share these properties with the Dirac matrices, but no explicit matrix representation is utilized in STA.
This generates a basis of one scalar, four vectors, six bivectors, four pseudovectors and one pseudoscalar .
Read more about this topic: Spacetime Algebra
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