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Physica Scripta
Article . 2023 . Peer-reviewed
License: IOP Copyright Policies
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2023
License: CC BY
Data sources: Datacite
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Unification of the four forces in the Spin(11,1) geometric algebra

Authors: Andrew J S Hamilton; Tyler McMaken;

Unification of the four forces in the Spin(11,1) geometric algebra

Abstract

Abstract SO(10), or equivalently its covering group Spin(10), is a well-known promising grand unified group that contains the standard-model group. The spinors of the group Spin(N) of rotations in N spacetime dimensions are indexed by a bitcode with [N/2] bits. Fermions in Spin(10) are described by five bits yzrgb, consisting of two weak bits y and z, and three colour bits r, g, b. If a sixth bit t is added, necessary to accommodate a time dimension, then the enlarged Spin(11, 1) algebra contains the standard-model and Dirac algebras as commuting subalgebras, unifying the four forces. The minimal symmetry breaking chain that breaks Spin(11, 1) to the standard model is unique, proceeding via the Pati-Salam group. The minimal Higgs sector is similarly unique, consisting of the dimension 66 adjoint representation of Spin(11, 1); in effect, the scalar Higgs sector matches the vector gauge sector. Although the unified algebra is that of Spin(11, 1), the persistence of the electroweak Higgs field after grand symmetry breaking suggests that the gauge group before grand symmetry breaking is Spin(10, 1), not the full group Spin(11, 1). The running of coupling parameters predicts that the standard model should unify to the Pati-Salam group Spin(4) w × Spin(6) c at 1012 GeV, and thence to Spin(10, 1) at 1015 GeV. The grand Higgs field breaks t-symmetry, can drive cosmological inflation, and generates a large Majorana mass for the right-handed neutrino by flipping its t-bit. The electroweak Higgs field breaks y-symmetry, and generates masses for fermions by flipping their y-bit.

Keywords

High Energy Physics - Theory, Physics - General Physics, General Physics (physics.gen-ph), High Energy Physics - Theory (hep-th), FOS: Physical sciences

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Green