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The Transwedge Product

The Transwedge Product

5 comments

·May 23, 2025
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senderista

I haven't seen any reason to believe that geometric algebra offers any real advantages for physics over ordinary exterior algebra and differential forms, and almost all theoretical physicists seem to agree with me. Am I missing something?

elengyel

I don't think you're missing anything. One of the goals of this article is to demonstrate how geometric algebra is really just another part of exterior algebra anyway. However, performing transformations in spacetime with the geometric product might make some things easier to understand, but I'm not making any strong claims about that. This article contains a small glimpse of what I'm talking about: https://terathon.com/blog/relativistic-quaternions.html

hamish_todd

Since Geometric Algebra == Clifford Algebra, Michael Atiyah, Roger Penrose, and Paul Dirac disagree with you.

senderista

If you're referring to spinors, those can be formalized without Clifford algebras (e.g. as fiber bundles). Can you show me any papers from these scientists that explicitly reference Clifford algebras?

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