Spacetime Algebra STA

In the context of Geometric Algebra, the Spacetime Algebra (STA) is a particular geometric algebra that is used to describe spacetime in the context of special relativity. STA is a 4D geometric algebra that is generated by the basis vectors $γ_{0}, γ_{1}, γ_{2}, γ_{3}$ and the geometric product generated by the following relations:

γ_{μ} \cdot γ_{ν} = η_{μ ν} = d i a g (1, - 1, - 1, - 1)

From these basis vectors we construct the basis of bivectors:

{γ_{0} γ_{1}, γ_{0} γ_{2}, γ_{0} γ_{3}, γ_{1} γ_{2}, γ_{1} γ_{3}, γ_{2} γ_{3}},

and the trivectors

{γ_{0} γ_{1} γ_{2}, γ_{0} γ_{1} γ_{3}, γ_{0} γ_{2} γ_{3}, γ_{1} γ_{2} γ_{3}} .

Finally, the pseudoscalar is given by

I = γ_{0} γ_{1} γ_{2} γ_{3} .

This algebra contains in a natural way the Algebra of Physical Space (APS). We can define

σ_{i} = γ_{i} γ_{0},

and it turns out that the $σ_{i}$ play the role of the vectors which generate the Algebra of Physical Space.