Leaderboard

Yes, it’s possible to do this, since both bispinors and rank-n tensors are possible representations of the Lorentz group. Essentially, you replace the bispinor by an ordinary 4-vector, and replace the gamma matrices by rank-3 tensors. So what you’re really doing is shift some of the transformation properties concerning rotations - encoded in the bispinor - into the gamma matrices themselves. The result can be shown to be physically equivalent to the ordinary Dirac bispinor formalism. For example: https://www.researchgate.net/publication/1898363_Dirac_Equation_Representation_Independence_and_Tensor_Transformation But why would you want to do this, I wonder? Bispinors already transform in the same way as tensors, so they are tensor-like objects - unsurprisingly, since both objects are representations of the Lorentz group.

Over 2000 nuclear explosions since 1945. A large number above ground. The Earth is still habitable. I don't mean to make light of the situation or possibility, but quit being such a pessimist 🙂 . ( I'll take my chances; I don't want to be at ground 0 )

I hate to tell you this but it is just about impossible to learn any technical subject topic by topic. This is particularly true for Mathematics. The reason for this is that all the topics are inter-related. You need to know a little bit of arithmetics to study algebra and a little bit of algebra to study geometry, but also a little bit of geometry at the beginning of algebra and so on. That is why the the same topics are revisited at every grade, but at a higher level.