Abstract
We demonstrate a model which captures certain attractive features of SU(5) theory, while providing a possible escape from proton decay. In this paper we show how ladder operators arise from the division algebras mathbb {R}, mathbb {C}, mathbb {H}, and mathbb {O}. From the SU(n) symmetry of these ladder operators, we then demonstrate a model which has much structural similarity to Georgi and Glashow’s SU(5) grand unified theory. However, in this case, the transitions leading to proton decay are expected to be blocked, given that they coincide with presumably forbidden transformations which would incorrectly mix distinct algebraic actions. As a result, we find that we are left with G_{sm} = SU(3)_Ctimes SU(2)_Ltimes U(1)_Y / mathbb {Z}_6. Finally, we point out that if U(n) ladder symmetries are used in place of SU(n), it may then be possible to find this same G_{sm}=SU(3)_Ctimes SU(2)_Ltimes U(1)_Y / mathbb {Z}_6, together with an extra U(1)_X symmetry, related to B!-!L.
Highlights
From a wide range of possible theories, the standard model has emerged almost uniquely, after having survived decades of experimental scrutiny
Upon closer inspection, we argue that SU (5) symmetry should never be fully realised in this division algebraic construction
We find that the stable subspaces of this division algebraic model exhibit the behaviour of one full generation of quarks and leptons, supplemented with a right-handed neutrino
Summary
From a wide range of possible theories, the standard model has emerged almost uniquely, after having survived decades of experimental scrutiny. The group SU (5) is the smallest simple Lie group to contain Gsm, admit complex representations, accommodate the standard model’s particle content, and be free of anomalies [1,2]. The exterior algebra ΛC5 breaks down into the 1 ⊕ 5 ⊕ 10 ⊕ 10∗ ⊕ 5∗ ⊕ 1 irreducible representations of SU (5) This successfully compiles a full generation of quarks and leptons into a single object, ΛC5, while accounting for their anti-particles, and including a right-handed neutrino.. This paper contributes to the existing literature by exposing a rather straightforward path from R, C, H, and O to the standard model’s gauge group, SU (3)C × SU (2)L × U (1)Y /Z6, with the possibility of an extra U (1)X symmetry, related to B − L. The possibility of an extra B−L symmetry mentioned here is exciting given the recent findings of [41,42,43,44]
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