Spacetime Algebra

In mathematical physics, spacetime algebra (STA) is a name for the Clifford algebra Cℓ_1,3(R), or equivalently the geometric algebra G₄ = G(M4), which can be particularly closely associated with the geometry of special relativity and relativistic spacetime.

It is a linear algebra allowing not just vectors, but also directed quantities associated with particular planes (for example: areas, or rotations) or associated with particular (hyper-)volumes to be combined, as well as rotated, reflected, or Lorentz boosted. It is also the natural parent algebra of spinors in special relativity. These properties allow many of the most important equations in physics to be expressed in particularly simple forms, and can be very helpful towards a more geometric understanding of their meanings.