Causal Fermion Systems and Octonions
arXiv:2403.00360 · doi:10.1002/prop.202400055
Abstract
We compare the structures and methods in the theory of causal fermion systems with approaches to fundamental physics based on division algebras, in particular the octonions. We find that octonions and, more generally, tensor products of division algebras come up naturally to describe the symmetries of the vacuum configuration of a causal fermion system. This is achieved by associating the real and imaginary octonion basis elements with the neutrino and charged sectors of the vacuum fermionic projector, respectively. Conversely, causal fermion systems provide octonionic theories with spacetime structures and dynamical equations via the causal action principle. In this way, octonionic theories and causal fermion systems complement each other..
36 pages, LaTeX, 1 figure, minor improvements (published version)
References in corpus (43)
- The Early Mirror Universe: Inflation, Baryogenesis, Nucleosynthesis and Dark Matter
- Mirror particles and mirror matter: 50 years of speculation and search
- Mirror World and its Cosmological Consequences
- Structure Formation with Mirror Dark Matter: CMB and LSS
- Mirror dark matter and large scale structure
- External Inversion, Internal Inversion, and Reflection Invariance
- Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra
- Exceptional quantum geometry and particle physics
- Gravitational origin of the weak interaction's chirality
- Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra
- Gravitational waves from dark first order phase transitions and dark photons
- A Lorentzian Quantum Geometry
- Through the Looking-Glass: Alice's Adventures in Mirror World
- Exceptional quantum geometry and particle physics II
- Dimensional Reduction
- Octonions, exceptional Jordan algebra and the role of the group F_4 in particle physics
- The Continuum Limit of Causal Fermion Systems
- Three fermion generations with two unbroken gauge symmetries from the complex sedenions
- Resonant Neutrino Self-Interactions
- Causal Fermion Systems as a Candidate for a Unified Physical Theory
- Local U(2,2) Symmetry in Relativistic Quantum Mechanics
- The standard model, the Pati-Salam model, and "Jordan geometry"
- Gravitational footprints of massive neutrinos and lepton number breaking
- A Hamiltonian Formulation of Causal Variational Principles
- Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
- Towards the map of quantum gravity
- Causal Fermion Systems: A Primer for Lorentzian Geometers
- Complex Structures on Jet Spaces and Bosonic Fock Space Dynamics for Causal Variational Principles
- Perturbative Description of the Fermionic Projector: Normalization, Causality and Furry's Theorem
- Emergent Photons and Gravitons:The Problem of Vacuum Structure
- Octions: An description of the Standard Model
- Gravitation, and quantum theory, as emergent phenomena
- Perturbation Theory for Critical Points of Causal Variational Principles
- Linearized Fields for Causal Variational Principles: Existence Theory and Causal Structure
- Why do elementary particles have such strange mass ratios? -- The role of quantum gravity at low energies
- Limiting Majoron self-interactions from Gravitational waves experiments
- Three generations of colored fermions with family symmetry from Cayley-Dickson sedenions
- Quantum theory without classical time: octonions, and a theoretical derivation of the fine structure constant 1/137
- Octonions, trace dynamics and non-commutative geometry: a case for unification in spontaneous quantum gravity
- Theoretically motivated dark electromagnetism as the origin of relativistic MOND
- Entangled Quantum States of Causal Fermion Systems and Unitary Group Integrals
- Modified Measures as an Effective Theory for Causal Fermion Systems
- Trace dynamics, and a ground state in spontaneous quantum gravity