Octonionic Kerzman–Stein Operators

An Octonionic Gauge Theory

The nonassociativity of the octonion algebra necessitates a bimodule representation, in which each element is represented by a left and a right multiplier. This representation can then be used to generate gauge transformations for the purpose of constructing a field theory symmetric under a gauged octonion algebra, the nonassociativity of which appears as a failure of the representation to clos...

Octonionic Aspects of Supergravity

Octonionic Gravitational Instantons

We construct eight-dimensional gravitational instantons by solving appropriate selfduality equations for the spin-connection. The particular gravitational instanton we present has Spin(7) holonomy and, in a sense, it is the eight-dimensional analog of the Eguchi-Hanson 4D space. It has a removable bolt singularity which is topologically S4 and its boundary at infinity is the squashed S7. We als...

Octonionic Binocular Mobilevision.

This paper is a compact overview of the heuristic approach to the recently elaborated octonionic binocular mobilevision [1]. 1. Interpretational geometries, anomalous virtual realities, and mobilevision 1.1. Interpretational geometry. A geometry being described below is related to a certain class of interactive information systems. Namely, let us call interactive information system computer– gr...

Octonionic Reformulation of Vector Analysis

According to celebrated Hurwitz theorem, there exists four division algebras consisting of R (real numbers), C (complex numbers), H (quaternions) and O (octonions). Keeping in view the utility of octonion variable we have tried to extend the three dimensional vector analysis to seven dimensional one. Starting with the scalar and vector product in seven dimensions, we have redefined the gradient...