2020年10月30日 · The octonions arise because in 8-dimensional Euclidean space - and only in 8 dimensions - there's a symmetry between vectors, right-handed spinor and left-handed spinors, called triality. This has big ramifications for 10-dimensional Minkowski spacetime: a vector is a self-adjoint matrix of octonions, while a left-handed or right-handed ...

2009年12月6日 · Nicolai digs back into string theory--supergravity, E8, octonions Hermann Nicolai is an interesting researcher to watch for several reasons. He is a leader in theoretical particle physics. Has been on the main advisory committee for the annual Strings conference for the last 10 years or so. A leader in the String community.

2024年8月4日 · Octonions and the Standard Model 3. How a lepton and a quark fit together into an octonion - at least if we only consider them as representations of SU(3), the gauge group of the strong force. Proof that the symmetries of the octonions fixing an imaginary octonion form precisely the group SU(3). Octonions and the Standard Model 4.

2010年10月16日 · Octonions Jonathan Hackett, Louis Kauffman 11 pages, 11 figures (Submitted on 14 Oct 2010) "In this paper we review the topological model for the quaternions based upon the Dirac string trick. We then extend this model, to create a model for the octonions - the non-associative generalization of the quaternions." This is primarily a math paper.

2004年8月24日 · Quaternions & Octonions: Definition & Uses Thread starter marlon; Start date Aug 24, 2004; Tags

2014年11月5日 · Your mentioning (matrices of) octonions reminded me (via matrices of quaternions) of the paper that came out yesterday by Chamseddine Connes Mukhanov. It employs 2-by-2 matrices of quaternions. I can't imagine any connection with E10, but this CCM paper got me curious because it proposes a way to "reconstruct, using the spectral action, the ...

2011年6月4日 · Shortly after the fantastic experimental success of Dirac's approach of using spinors to model the degrees of freedom of electron motion, Mayer and Einstein studied how they fit into and were required by the symmetry demands of relativistic covariance: A. Einstein and W. Mayer, Preuss, Akad. Wiss. Phys. Math. Klass.

2022年9月18日 · Quaternions and Octonions. The complex numbers can be visualized as points in the complex plane because ##\mathbb{C}=\mathbb{R}+i\cdot\mathbb{R},## and Sir William Rowan Hamilton (1805 – 1865) spent years figuring out a similar construction for the three-dimensional space. He failed. But at least he found a four-dimensional construction $$

2004年8月27日 · In summary, there are numbers called sedenions that have 15 imaginary parts and 1 real part. However, they do not form a division algebra and are obtained by performing the Cayley-Dickenson construction on octonions. We can continue this construction to create algebras with even higher dimensions.

2022年4月5日 · https://events.perimeterinstitute.ca › event › overviewFeb 8, 2021 — Over the years, various researchers have suggested connections between the octonions and the standard model of particle physics. In this talk we review some lessons from grand unified theories and also from recent work using the octonions. The gauge group of the Standard...