Has anyone done work on a projectivized version of Spacetime Algebra? I’m thinking of spaces with a signature like (1,3,1) or (3,1,1). The motivation would be so that the whole Poincare group (rotations, Lorentz boosts, and translations) could be represented by versors without the extra bits needed for a conformal picture. In other words, an algebra for flats in Special Relativity.
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i am also interested in this.
Waiting for it as well 
Hi. I’ve been trying to read Sokolov’s paper on projective Minkowski space and have suspicions about the treatment of bivectors and trivectors. For example he uses the regressive product to define a line, but it seems to me that the outer product is what should be used.
But the biggest question that I have is defining the force multivector for Maxwells equations. Should it be a line joining P and P(t+dt), or an osculating plane joining three nearby points (ie a bivector). Also the connection with the rotor view.
This is all amateur activity during the pandemic.