Related papers: A Royal Road to Quantum Theory (or Thereabouts)
We develop a theory of quantum sufficiency on real *-subalgebras and real Jordan algebras. In contrast to the conventional formulation, which is based on families of states, complex completely positive coarse-grainings, and Radon-Nikodym…
Two novel frameworks for handling mathematical and physical problems are introduced. The first, the emerging Jordan form, generalizes the concept of the Jordan canonical form, a well-established tool of linear algebra. The second, dual…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual…
The fundamental identity of quadratic Jordan algebras $Q_{Q_a b} = Q_aQ_bQ_a$ is commonly proven as a consequence of MacDonalds theorem or using more analytic methods. In this short note we give a self-contained purely algebraic proof using…
We review attempts by Pascual Jordan and other researchers, most notably Lawrence Biedenharn to generalize quantum mechanics by passing from associative matrix or operator algebras to non-associative algebras. We start with Jordan's work…
Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group $SU(3)$ and on the existence of 3 generations, we develop an argumentation suggesting that the "finite quantum space" corresponding to…
We review work classifying the physically distinct forms of 3-qubit entanglement using the elegant framework of Jordan algebras, Freudenthal triple systems and groups of type E_7. While this framework is, in the first instance, specific to…
With this paper we start a programme aiming at connecting two vast scientific areas: Jordan algebras and representation theory. Within representation theory, we focus on non-compact, real forms of semisimple Lie algebras and groups as well…
We argue that the quantum-theoretical structures studied in several recent lines of research cannot be adequately described within the standard framework of quantum circuits. This is in particular the case whenever the combination of…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Feynman path integrals formalism for non-relativistic quantum mechanics is revisited. A comparison is made with the cases of light progagation (Huygens principle) and Brownian motion. The difficulties for a physical model behind Feynman…
The metohod of ortogonal rotations introduced in the previous papers of the author is used for construction of the explicit form the generators of the simple roots for quantum (and ussual) semisimple algebras. All calculations are presented…
We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content…
The author introduces the notion of a quantum form of an algebraic torus. In the case of diagonal algebraic torus we get the algebra of Laurent twisted polynomials. Quantum algebraic torus can be characterized in terms of exact sequences.…
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…
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 interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time and most advanced results are due to Alfsen and Shultz. Here we…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard…