# Angular momentum and torque described with the complex octonion

## Abstract

The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum (or torque, force) to combine some physics contents, which were considered to be independent of each other in the past. J. C. Maxwell used simultaneously two methods, the vector terminology and quaternion analysis, to depict the electromagnetic theory. It motivates the paper to introduce the quaternion space into the field theory, describing the physical feature of electromagnetic and gravitational fields. The spaces of electromagnetic field and of gravitational field can be chosen as the quaternion spaces, while the coordinate component of quaternion space is able to be the complex number. The quaternion space of electromagnetic field is independent of that of gravitational field. These two quaternion spaces may compose one octonion space. Contrarily, one octonion space can be separated into two subspaces, the quaternion space and S-quaternion space. In the quaternion space, it is able to infer the field potential, field strength, field source, angular momentum, torque, and force etc in the gravitational field. In the S-quaternion space, it is capable of deducing the field potential,more »

- Authors:

- School of Physics and Mechanical and Electrical Engineering, Xiamen University, Xiamen 361005 (China)

- Publication Date:

- OSTI Identifier:
- 22299790

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Advances; Journal Volume: 4; Journal Issue: 8; Other Information: (c) 2014 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; CONTINUITY EQUATIONS; DIPOLE MOMENTS; ELECTROMAGNETIC FIELDS; FIELD THEORIES; GRAVITATIONAL FIELDS

### Citation Formats

```
Weng, Zi-Hua, E-mail: xmuwzh@xmu.edu.cn.
```*Angular momentum and torque described with the complex octonion*. United States: N. p., 2014.
Web. doi:10.1063/1.4892165.

```
Weng, Zi-Hua, E-mail: xmuwzh@xmu.edu.cn.
```*Angular momentum and torque described with the complex octonion*. United States. doi:10.1063/1.4892165.

```
Weng, Zi-Hua, E-mail: xmuwzh@xmu.edu.cn. Fri .
"Angular momentum and torque described with the complex octonion". United States.
doi:10.1063/1.4892165.
```

```
@article{osti_22299790,
```

title = {Angular momentum and torque described with the complex octonion},

author = {Weng, Zi-Hua, E-mail: xmuwzh@xmu.edu.cn},

abstractNote = {The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum (or torque, force) to combine some physics contents, which were considered to be independent of each other in the past. J. C. Maxwell used simultaneously two methods, the vector terminology and quaternion analysis, to depict the electromagnetic theory. It motivates the paper to introduce the quaternion space into the field theory, describing the physical feature of electromagnetic and gravitational fields. The spaces of electromagnetic field and of gravitational field can be chosen as the quaternion spaces, while the coordinate component of quaternion space is able to be the complex number. The quaternion space of electromagnetic field is independent of that of gravitational field. These two quaternion spaces may compose one octonion space. Contrarily, one octonion space can be separated into two subspaces, the quaternion space and S-quaternion space. In the quaternion space, it is able to infer the field potential, field strength, field source, angular momentum, torque, and force etc in the gravitational field. In the S-quaternion space, it is capable of deducing the field potential, field strength, field source, current continuity equation, and electric (or magnetic) dipolar moment etc in the electromagnetic field. The results reveal that the quaternion space is appropriate to describe the gravitational features, including the torque, force, and mass continuity equation etc. The S-quaternion space is proper to depict the electromagnetic features, including the dipolar moment and current continuity equation etc. In case the field strength is weak enough, the force and the continuity equation etc can be respectively reduced to that in the classical field theory.},

doi = {10.1063/1.4892165},

journal = {AIP Advances},

number = 8,

volume = 4,

place = {United States},

year = {Fri Aug 15 00:00:00 EDT 2014},

month = {Fri Aug 15 00:00:00 EDT 2014}

}