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Real Clifford Algebras and Their Spinors for Relativistic Fermions [PDF]
Universe, 2021 Real Clifford algebras for arbitrary numbers of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed.
Stefan Floerchinger
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The birth of E8 out of the spinors of the icosahedron. [PDF]
Proc Math Phys Eng Sci, 2016 $E_8$ is prominent in mathematics and theoretical physics, and is generally viewed as an exceptional symmetry in an eight-dimensional space very different from the space we inhabit; for instance the Lie group $E_8$ features heavily in ten-dimensional ...
Dechant PP.
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Clifford algebras, spinors and fundamental interactions : Twenty Years After [PDF]
Advances in Applied Clifford Algebras, 2005 This is a short review of the algebraic properties of Clifford algebras and spinors. Their use in the description of fundamental physics (elementary particles) is also summarized.
Coquereaux, Robert
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Topological preons from algebraic spinors
European Physical Journal C: Particles and Fields, 2021 It is demonstrated that many of the assumed rules that govern the structure of a previously proposed topological preon model, in which simple non-trivial braids consisting of three twisted ribbons are mapped to the first generation of leptons and quarks,
Niels G. Gresnigt
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Octonion Internal Space Algebra for the Standard Model
Universe, 2023 This paper surveys recent progress in our search for an appropriate internal space algebra for the standard model (SM) of particle physics. After a brief review of the existing approaches, we start with the Clifford algebras involving operators of left ...
Ivan Todorov
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Subliminal aspects concerning the Lounesto’s classification
European Physical Journal C: Particles and Fields, 2020 In the present communication we employ a split programme applied to spinors belonging to the regular and singular sectors of the Lounesto’s classification (Clifford algebras and spinors, Cambridge University Press, Cambridge), looking towards unveil how ...
R. J. Bueno Rogerio
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Clifford algebras, algebraic spinors, quantum information and applications [PDF]
Modern Physics Letters A, 2020 We give an algebraic formulation based on Clifford algebras and algebraic spinors for quantum information. In this context, logic gates and concepts such as chirality, charge conjugation, parity and time reversal are introduced and explored in connection with states of qubits.
Trindade, Marco A. S. +2 more
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A binary encoding of spinors and applications
Complex Manifolds, 2020 We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations.
Arizmendi Gerardo, Herrera Rafael
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Quaternionic and Octonionic Spinors. A Classification [PDF]
, 2003 Quaternionic and octonionic realizations of Clifford algebras and spinors are classified and explicitly constructed in terms of recursive formulas. The most general free dynamics in arbitrary signature space-times for both quaternionic and octonionic ...
C.A. Barton +29 more
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Algebraic spinors on Clifford manifolds [PDF]
Journal of Physics A: Mathematical and General, 2002 Summary: A Clifford manifold of \(n\) dimensions is defined by the fundamental relation \[ \{\mathbf e_{\mu}(x), \mathbf e_{\nu}(x)\} = 2g_{\mu \nu}(x)\mathbf 1 \] between the \(n\) frame field components \(\{\mathbf e_{\mu}(x)\}\) and the metric matrix \(\{g_{\mu \nu}(x)\}\). At any point \(x\), the tangent space, orthonormal frames and the spin group
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