Exponential forms and wavefunctions of the octonion angular momenta

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.