Title: Standard model irreps as an extension of 4-momentum: our first attempt

Abstract: In modern formalisms, 4-momenta are often described as 2×2 hermitian matrices, H_2(C). Here we propose embedding the standard model’s full set of irreducible representations inside its extension, H_16(C). Generating this H_16(C) from the division algebras facilitates its fragmentation into blocks (a Peirce decomposition). We demonstrate an embedding of a majority of the standard model’s unconstrained SU(3)xSU(2)xU(1) / Z_6 irreps which is (1) nearly surjective, and (2) largely obeys an octonionic Peirce decomposition. Momenta and bosons (covariant derivative) appear on the diagonal blocks, while fermions appear on the off-diagonals. Peirce idempotents correspond to projective measurement operators, and we observe that a natural division algebraic choice of Peirce idempotents omits colour as an observable. Finally, we identify a possible niche for a vierbein. With all this said, a simple description for the electroweak sector is (frustratingly) still wanting. The material is based on joint work with Beth Romano.

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