Exponential forms and wavefunctions of the octonion angular momenta

- Zi-Hua Weng

## Abstract

The paper aims to explore the exponential forms of octonion angular
momenta in the electromagnetic and gravitational fields, researching the
influencing factors and physical properties of octonion wavefunctions.
J. C. Maxwell first utilized the quaternions and vectorial terminology
to describe the electromagnetic theory. Nowadays, the scholars apply the
quaternions and octonions to study the electromagnetic fields,
gravitational fields, and quantum mechanics and so forth. The
application of octonions is able to describe the physical quantities of
electromagnetic fields and gravitational fields, including the octonion
field strength, field source, linear momentum, angular momentum, torque,
and force and others. According to the characteristics of octonions, the
octonion physical quantities can be rewritten into the exponential
forms. In particular, either the angular momentum or electromagnetic
moment may be dominant under certain circumstances, in the octonion
spaces. The product of the octonion angular momentum and Planck's
constant can constitute a nondimensionalized octonion exponential form.
As a result, the octonion wavefunctions can be obtained from the
exponential forms of octonion angular momenta. When the direction of
multidimensional unit vector in the octonion wavefunction cannot be
determined, the imaginary unit can be used to substitute the
multidimensional unit vector. As a compensation measure, it is necessary
to replace one single octonion wavefunction, relevant to a
multidimensional unit vector, with several wavefunctions related to the
imaginary units. The dimension number of unit vector may be interrelated
to the color number of color charges in the quantum chromodynamics.