On the value of geometric algebra for spacetime analyses using an investigation of the form of the self-force on an accelerating charged particle as a case study

Rowland, David R. (2010) On the value of geometric algebra for spacetime analyses using an investigation of the form of the self-force on an accelerating charged particle as a case study. American Journal of Physics, 78 2: 187-194.


Author Rowland, David R.
Title On the value of geometric algebra for spacetime analyses using an investigation of the form of the self-force on an accelerating charged particle as a case study
Journal name American Journal of Physics   Check publisher's open access policy
ISSN 0002-9505
Publication date 2010-02
Sub-type Article (original research)
DOI 10.1119/1.3265546
Volume 78
Issue 2
Start page 187
End page 194
Total pages 8
Place of publication College Park, MD, U.S.A.
Publisher American Association of Physics Teachers
Collection year 2011
Language eng
Abstract The ability to treat vectors in classical mechanics and classical electromagnetism as single geometric objects rather than as a set of components facilitates physical understanding and theoretical analysis. To do the same in four-dimensional spacetime calculations requires a generalization of the vector cross product. Geometric algebra provides such a generalization and is much less abstract than exterior forms. It is shown that many results from geometric algebra are useful for spacetime calculations and can be presented as simple extensions of conventional vector algebra. As an example, it is shown that geometric algebra tightly constrains the possible forms of the self-force that an accelerating charged particle experiences and predicts the Lorentz–Abraham–Dirac equation of motion up to a constant of proportionality. Geometric algebra also makes the important physical content of the Lorentz–Abraham–Dirac equation more transparent than does the standard tensor form of this equation, thus allowing a proposed modification to this equation free from the problems of preacceleration and runaway motion to be easily predicted.
Keyword classical mechanics
electromagnetism
geometry
physics education
space-time configurations
vectors
Radiation Reaction
Electrodynamics
Physics
Fields
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: UQ staff Publications
Official 2011 Collection
 
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Created: Sun, 31 Jan 2010, 00:07:28 EST