Related papers: The standard model, the Pati-Salam model, and "Jor…
We put forward a definition for spectral triples and algebraic backgrounds based on Jordan coordinate algebras. We also propose natural and gauge-invariant bosonic configuration spaces of fluctuated Dirac operators and compute them for…
Jordan, Wigner and von Neumann classified the possible algebras of quantum mechanical observables, and found they fell into 4 "ordinary" families, plus one remarkable outlier: the exceptional Jordan algebra. We point out an intriguing…
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain…
Jordan algebras were first introduced in an effort to restructure quantum mechanics purely in terms of physical observables. In this paper we explain why, if one attempts to reformulate the internal structure of the standard model of…
We propose a model for the universe based on Jordan algebras. The action consists of cubic terms with coefficients being the structure constants of a Jordan algebra. Coupling constants only enter the theory via symmetry breaking which also…
Starting from an abstract setting for the Lueders - von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of…
The product of two Heisenberg-Weil algebras contains the Jordan-Schwinger representation of su(2). This Algebra is quotiented by the square-root of the Casimir to produce a non-associative algebra denoted by $\Psi$. This algebra may be…
Noncommutative geometry, in its many incarnations, appears at the crossroad of various researches in theoretical and mathematical physics: from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and…
The exceptional Jordan algebra is the algebra of $3\times 3$ Hermitian matrices with octonionic entries. It is the only one from Jordan's algebraic formulation of quantum mechanics which is not equivalent to the conventional formulation of…
We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in particular. This defines the framework of…
I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the…
In this paper, we develop a method to obtain the algebraic classification of noncommutative Jordan algebras from the classification of Jordan algebras of the same dimension. We use this method to obtain the algebraic classification of…
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems.…
Symmetry postulates play a crucial role in various approaches to reconstruct quantum theory from a few basic principles. Discrete and continuous symmetries are under consideration. The continuous case better matches the physical needs for…
The aim of this paper is to offer an overview of the most important applications of Jordan structures inside mathematics and also to physics, up-dated references being included. For a more detailed treatment of this topic see - especially -…
This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature)…
We review the construction of particle physics models in the framework of non-commutative geometry. We first give simple examples, and then progress to outline the Connes-Lott construction of the standard Weinberg-Salam model and our…
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 takes over the role of $i$ times the…
The assumption that space-time is a noncommutative space formed as a product of a continuous four dimensional manifold times a finite space predicts, almost uniquely, the Standard Model with all its fermions, gauge fields, Higgs field and…
D. Benkovi\v{c} described Jordan homomorphisms of algebras of triangular matrices over a commutative unital ring without additive $2$-torsion. We extend this result to the case of noncommutative rings and remove the assumption of additive…