Related papers: Trace dynamics, octonions, and unification: An $E_…
There must exist a reformulation of quantum field theory, even at low energies, which does not depend on classical time. The octonionic theory proposes such a reformulation, leading to a pre-quantum pre-spacetime theory. The ingredients for…
The $E_8 \times \omega E_8$ octonionic program aims at a deliberately ambitious synthesis: quantum theory without external classical time, objective collapse, emergent classical space-time, exceptional Jordan-algebra flavor structure, and…
In considering the nature of the basic mathematical structures appropriate for describing the fundamental elements of particle physics a significant role for the octonions, as an extension from the complex numbers and uniquely the largest…
Various problems of mathematical physics consider octonions and split-octonions as a mathematical structure, which underpins the eight-dimensional nature of these problems. Therefore, it is not surprising that octonionic analysis has become…
We present a framework having the potential to unify the fundamental interactions in nature by introducing new degrees of freedom. An attempt is made to explain the hierarchy between the weak scale and the coupling unification scale, which…
In these lectures we review the motivation, principles of and (circumstantial) evidence for the program of unification of the fundamental forces. In an appendix, we review the group theory pertinent to the program.
In recent years, there is a growing interest in the studying octonions, which are 8-dimensional hypercomplex numbers forming the biggest normed division algebras over the real numbers. In particular, various tools of the classical complex…
In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.
Based upon the unique and simple starting point of the continuous flow of time a physical theory is derived through an analysis of the elementary arithmetic composition and symmetries of this one-dimensional progression. We describe how the…
We review, in a historical perspective, developments in physics which led to the emergence of unifying ideas and theories. Some attention is paid to the theoretical programme that started in the second decade of the XXth century and whose…
We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe physical signals. The new geometrical interpretation of the products of octonionic basis units is presented.…
An attempt has been made to analyse the the role of octonions in various unified field theories associated with dyons and the dark matter. Starting with the split octonion al- gebra and its properties, we have discussed the octonionic…
The unified theory of physics unifies various phenomena in our observable universe and other universes. The unified theory is based on the zero-energy universe and the space-object structures. Different universes in different developmental…
We introduce a fundamental theory for the kinetics of systems of classical particles. The theory represents a unification of kinetic theory, Brownian motion and field theory. It is self-consistent and is the dynamic generalization of the…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are…
We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the…
Demonstrating the split octonion formalism for unified fields of dyons (electromagnetic fields) and gravito-dyons (gravito-Heavisidian fields of linear gravity), relevant field equations are derived in compact, simpler and manifestly…
A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…
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…