Quark structure and octonions

Günaydın, Murat; Gürsey, Feza

doi:10.1063/1.1666240

Cited by 341 publications

(412 citation statements)

References 30 publications

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“…The early work of Günaydin and Gürsey, [1,2] shows a representation of the Lie algebra LG 2 in terms of sequences of octonions acting on octonions. Here, gauge bosons are unified with fermions.…”

Section: Jhep10(2014)046mentioning

confidence: 99%

“…Here, gauge bosons are unified with fermions. Extending the work of [1] was Dixon, [3,4], who then suggested writing all fermionic degrees of freedom in terms of the tensor product of the division algebras. Local spacetime degrees of freedom are unified with internal degrees of freedom.…”

Section: Jhep10(2014)046mentioning

confidence: 99%

“…It may prompt investigators to reinvest in early theories, [1]- [5], which are based on the idea of division algebras acting on themselves. It may provide important clues for those working on novel constructions of particle physics [6]- [9].…”

Section: Jhep10(2014)046mentioning

confidence: 99%

“…Clearly, Λ, as expressed above, constitutes an element of C ⊗ ← − O . In earlier references, [1][2][3][4], this Λ is shown to act on quark and lepton representations in the eight-dimensional C ⊗ O, or multiple copies thereof. In contrast, here we introduce Λ acting on quark and lepton representations of the 64-dimensional C ⊗ ← − O .…”

Section: Jhep10(mentioning

confidence: 99%

“…The above representation of su(3) can be found in [1], introduced as a subalgebra of LG 2 acting on the octonions. Clearly, Λ, as expressed above, constitutes an element of C ⊗ ← − O .…”

Section: Jhep10(mentioning

confidence: 99%

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Furey

2014

J. High Energ. Phys.

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We point out a somewhat mysterious appearance of SU c (3) representations, which exhibit the behaviour of three full generations of standard model particles. These representations are found in the Clifford algebra Cl(6), arising from the complex octonions. In this paper, we explain how this 64-complex-dimensional space comes about. With the algebra in place, we then identify generators of SU(3) within it. These SU(3) generators then act to partition the remaining part of the 64-dimensional Clifford algebra into six triplets, six singlets, and their antiparticles. That is, the algebra mirrors the chromodynamic structure of exactly three generations of the standard model's fermions. Passing from particle to antiparticle, or vice versa, requires nothing more than effecting the complex conjugate, * : i → −i. The entire result is achieved using only the eight-dimensional complex octonions as a single ingredient.

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Section: Jhep10(2014)046mentioning

confidence: 99%

Section: Jhep10(2014)046mentioning

confidence: 99%

Section: Jhep10(2014)046mentioning

confidence: 99%

Section: Jhep10(mentioning

confidence: 99%

Section: Jhep10(mentioning

confidence: 99%

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Furey

2014

J. High Energ. Phys.

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Hidden nonassociative structure in supersymmetric quantum mechanics

Dzhunushaliev

2010

Annalen der Physik

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Some recent results for SU(3) and octonions within the geometric algebra approach to the fundamental forces of nature

Lasenby

2023

Math Methods in App Sciences

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Different ways of representing the group within a Geometric Algebra approach are explored. As part of this, we consider characteristic multivectors for and how these are linked with decomposition of generators into commuting bivectors. The setting for this work is within a 6d Euclidean Clifford Algebra. We then go on to consider whether the fundamental forces of particle physics might arise from symmetry considerations in just the 4d geometric algebra of spacetime—the STA. As part of this, a representation of is found wholly within the STA, involving preservation of a bivector norm. We also show how Octonions can be fully represented within the Spacetime Algebra, which we believe will be useful in making them understandable and accessible to a new community in Physics and Engineering. The two strands of the paper are drawn together in showing how preserving the octonion norm is the same as preserving the timelike part of the Dirac current of a particle. This suggests a new model for the symmetries preserved in particle physics. Following on from work by Günaydin and Gürsey on the link between quarks, and octonions, and by Furey on chains of octonionic multiplications, we show how both of these fit well within our scheme and give some wholly STA versions of the operations involved, which in the cases considered have easily understandable equivalents in terms of 4d geometry. Links with larger groups containing , such as and , are also considered.

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Quark structure and octonions

Cited by 341 publications

References 30 publications

Generations: three prints, in colour

Generations: three prints, in colour

Hidden nonassociative structure in supersymmetric quantum mechanics

Some recent results for SU(3) and octonions within the geometric algebra approach to the fundamental forces of nature

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