Title of Oral/Poster Presentation

Quaternions, Octonions, and Electromagnetism

Presenter Information

Ben Shaw, Utah State University

Class

Article

College

College of Science

Department

Physics Department

Faculty Mentor

Charles Torre

Presentation Type

Oral Presentation

Abstract

An introduction to Quaternions and Octonions is given, and the Maxwell Equations are formulated in terms of each. The conventional, source-free relativistic theory of eight dimensional electromagnetism is introduced and examined. Similarly, the source-free Octonionic Maxwell Equations are developed, and it is shown that the seven dimensional electric and magnetic fields pure Octonions each admit plane wave solutions. An Octonionic Faraday tensor is constructed and compared with the conventional Faraday tensor, and it is shown that, in the source-free case, the conventional and Octonionic theories are equivalent.

Location

Room 154

Start Date

4-10-2019 9:00 AM

End Date

4-10-2019 10:15 AM

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Apr 10th, 9:00 AM Apr 10th, 10:15 AM

Quaternions, Octonions, and Electromagnetism

Room 154

An introduction to Quaternions and Octonions is given, and the Maxwell Equations are formulated in terms of each. The conventional, source-free relativistic theory of eight dimensional electromagnetism is introduced and examined. Similarly, the source-free Octonionic Maxwell Equations are developed, and it is shown that the seven dimensional electric and magnetic fields pure Octonions each admit plane wave solutions. An Octonionic Faraday tensor is constructed and compared with the conventional Faraday tensor, and it is shown that, in the source-free case, the conventional and Octonionic theories are equivalent.