I noticed a few sources that seem to indicate that Clifford algebra may be used in both QFT and GR. I've seen where the Clifford algebra is a type of associative algebra that generalizes the real numbers, complex numbers, quaternions, and octonions, see Wikipedia on Clifford Algebra. And I've seen where the complex numbers, quaternions, and octernions can be used in the description for the U(1), SU(2), SU(3) symmetries of the Standard Model, see this article, and this book. However, I've also seen where the Clifford algebra can be used in an alternative description of differential geometry used in the formulation of GR, see this book for example.(adsbygoogle = window.adsbygoogle || []).push({});

So my question is does this common algebra allow us to derive GR in terms of QFT or visa versa? Or if we could justify the use of the complex numbers, quaternions, octonions, and the Clifford algebra by some other means, could we derive both QFT and GR from that common justification of the algebra? What more information or constraints would be needed to do so?

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# Does Clifford algebra solve both QFT and GR

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