\(\mathbb{R} \otimes \mathbb{C}\otimes \mathbb{H}\otimes \mathbb{O}\)-valued gravity as a grand unified field theory

DOI10.1007/s00006-019-0937-4zbMath1410.81034OpenAlexW2918285367MaRDI QIDQ1728288

Carlos Castro Perelman

Publication date: 22 February 2019

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-019-0937-4

zbMATH Keywords

Clifford algebrasquaternionsstringsunificationnonassociative geometryoctonionic gravity

Mathematics Subject Classification ID

Unified quantum theories (81V22) String and superstring theories in gravitational theory (83E30) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Gravitational interaction in quantum theory (81V17) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Special relativity (83A05) Relativistic gravitational theories other than Einstein's, including asymmetric field theories (83D05) Clifford algebras, spinors (15A66)

Related Items

One generation of standard model Weyl representations as a single copy of \(\mathbb{R} \otimes \mathbb{C} \otimes \mathbb{H} \otimes \mathbb{O}\) ⋮ A topological model of composite preons from the minimal ideals of two Clifford algebras ⋮ Division algebraic symmetry breaking ⋮ Nonassociative Geometry of Nonholonomic Phase Spaces with Star R‐flux String Deformations and (non) Symmetric Metrics ⋮ Decoupling and Integrability of Nonassociative Vacuum Phase Space Gravitational Equations With Star and R‐flux Parametric Deformations ⋮ (Anti) de Sitter geometry, complex conformal gravity-Maxwell theory from a \(Cl(4, C)\) gauge theory of gravity and grand unification ⋮ On \(\mathbf{C} \otimes \mathbf{H} \otimes \mathbf{O}\)-valued gravity, sedenions, Hermitian matrix geometry and nonsymmetric Kaluza-Klein theory ⋮ On Jordan-Clifford algebras, three fermion generations with Higgs fields and a \(\mathrm{SU}(3) \times \mathrm{SU}(2)_L \times \mathrm{SU}(2)_R \times \mathrm{U}(1)\) model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Charge quantization from a number operator
• A Clifford \(Cl(5, C)\) unified gauge field theory of conformal gravity, Maxwell and \(U(4) \times U(4)\) Yang-Mills in \(4D\)
• Kaluza-Klein theory without extra dimensions: curved Clifford space
• The minimal unitary representation of \(E_{8(8)}\)
• Exceptional super Yang-Mills in 27 + 3 and worldvolume M-theory
• The large \(N\) limit of exceptional Jordan matrix models and M, F theory
• Supersymmetry in physics: an algebraic overview
• Moufang plane and octonionic quantum mechanics
• Clifford algebra of spacetime and the conformal group
• A taste of Jordan algebras
• Erratum to: Ghost-free infinite derivative gravity
• A polynomial Weyl-invariant spinning-membrane action
• Evidence for F-theory
• Quaternionic-valued gravitation in \(8D\), grand unification and Finsler geometry
• Spinning equations for objects of some classes in Finslerian geometry
• A generalization of the relativistic theory of gravitation. II
• ADVANCES IN TERNARY AND OCTONIONIC GAUGE FIELD THEORIES
• Lectures on F-theory compactifications and model building
• SPIN GAUGE THEORY OF GRAVITY IN CLIFFORD SPACE: A REALIZATION OF KALUZA–KLEIN THEORY IN FOUR-DIMENSIONAL SPACE–TIME
• The octic E8 invariant
• On the noncommutative and nonassociative geometry of octonionic space time, modified dispersion relations and grand unification
• An extension of quaternionic metrics to octonions
• Octonionic representations of GL(8,ℛ) and GL(4,𝒞)
• The octonions
• A supersymmetric grand unified model with noncompact horizontal symmetry
• Sp(4,H) / Z2 Pair Universe in E6 Matrix Models