## 53 Citations

### Exceptional Quantum Algebra for the Standard Model of Particle Physics

- Physics, MathematicsSpringer Proceedings in Mathematics & Statistics
- 2020

The exceptional euclidean Jordan algebra of 3x3 hermitian octonionic matrices, appears to be tailor made for the internal space of the three generations of quarks and leptons. The maximal rank…

### The Characteristic Equation of the Exceptional Jordan Algebra: Its Eigenvalues, and their relation with the Mass Ratios of Quarks and Leptons

- Mathematics
- 2021

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This pre-theory offers the prospect of unifying the internal…

### Quantum gravity effects in the infrared: a theoretical derivation of the low-energy fine structure constant and mass ratios of elementary particles

- PhysicsThe European Physical Journal Plus
- 2022

We have recently proposed a pre-quantum, pre-spacetime theory as a matrix-valued Lagrangian dynamics on an octonionic spacetime. This theory offers the prospect of unifying internal symmetries of the…

### The Standard Model Algebra - Leptons, Quarks, and Gauge from the Complex Clifford Algebra Cl6

- Mathematics
- 2017

A simple geometric algebra is shown to contain automatically the leptons and quarks of a family of the Standard Model, and the electroweak and color gauge symmetries, without predicting extra…

### Quantum gravity eﬀects in the infra-red: a theoretical derivation of the low energy ﬁne structure constant and mass ratios of charged fermions

- Physics
- 2022

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This theory oﬀers the prospect of unifying internal symmetries of…

### Color confinement at the boundary of the conformally compactified AdS5

- Physics, MathematicsJournal of High Energy Physics
- 2021

The topology of closed manifolds forces interacting charges to appear in pairs. We take advantage of this property in the setting of the conformal boundary of AdS5 spacetime, topologically equivalent…

### The Characteristic Equation of the Exceptional Jordan Algebra: Its Eigenvalues, and Their Possible Connection with the Mass Ratios of Quarks and Leptons

- Physics, Mathematics
- 2021

The exceptional Jordan algebra [also known as the Albert algebra] is the finite dimensional algebra of 3x3 Hermitean matrices with octonionic entries. Its automorphism group is the exceptional Lie…

### A remarkable dynamical symmetry of the Landau problem

- MathematicsJournal of Physics: Conference Series
- 2022

We show that the dynamical group of an electron in a constant magnetic feld is the group of symplectomorphisms Sp(4, R). It is generated by the spinorial realization of the conformal algebra so(2,3)…

### Trace dynamics and division algebras: towards quantum gravity and unification

- Physics
- 2020

Abstract We have recently proposed a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang–Mills fields, and fermions. Dynamical variables are described by odd-grade…

### Why Do Elementary Particles Have Such Strange Mass Ratios?—The Importance of Quantum Gravity at Low Energies †

- PhysicsPhysics
- 2022

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infra-red. Using the octonions as space-time…

## References

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- Mathematics
- 1979

It is shown that a Hilbert space over the real Clifford algebra C7 provides a mathematical framework, consistent with the structure of the usual quantum mechanical formalism, for models for the…

### Noncommutative differential geometry and new models of gauge theory

- Mathematics
- 1990

The noncommutative differential geometry of the algebra C∞(V)⊗Mn(C) of smooth Mn(C)‐valued functions on a manifold V is investigated. For n≥2, the analog of Maxwell’s theory is constructed and…

### Non-associative geometry and the spectral action principle

- Physics
- 2013

A bstractChamseddine and Connes have argued that the action for Einstein gravity, coupled to the SU(3) × SU(2) × U(1) standard model of particle physics, may be elegantly recast as the “spectral…

### On an Algebraic generalization of the quantum mechanical formalism

- Mathematics
- 1934

One of us has shown that the statistical properties of the measurements of a quantum mechanical system assume their simplest form when expressed in terms of a certain hypercomplex algebra which is…

### Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry

- Physics
- 2014

Connes’ non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a…

### Noncommutative Finite-Dimensional Manifolds. I. Spherical Manifolds and Related Examples

- Mathematics
- 2001

Abstract: We exhibit large classes of examples of noncommutative finite-dimensional manifolds which are (non-formal) deformations of classical manifolds. The main result of this paper is a complete…

### The Jordan formulation of Quantum Mechanics: a review

- Mathematics
- 2016

This is a transcription of a conference proceedings from 1985. It reviews the Jordan algebra formulation of quantum mechanics. A possible novelty is the discussion of time evolution; the associator…

### Moufang plane and octonionic Quantum Mechanics

- Physics, Mathematics
- 1978

It is shown that the usual axioms of one-particle Quantum Mechanics can be implemented with projection operators belonging to the exceptional Jordan algebraJ83 over real octonions. Certain lemmas on…

### The Spectral Action Principle

- Physics
- 1997

Abstract:We propose a new action principle to be associated with a noncommutative space . The universal formula for the spectral action is where is a spinor on the Hilbert space, is a scale and a…

### On the Role of Division, Jordan and Related Algebras in Particle Physics

- Mathematics
- 1996

Part 1 Quaternions: algebraic structures Jordan formulation, H-Hilbert spaces and groups vector products, parallelisms and quaternionic manifolds quaternionic function theory arithmetics of…