Skip to main content

Biquaternionic Formulation of Maxwell’s Equations and their Solutions

  • Chapter
Clifford Algebras and Spinor Structures

Part of the book series: Mathematics and Its Applications ((MAIA,volume 321))

Abstract

The theory of functions of a real biquaternion variable and the solutions of Maxwell’s equations are recapitulated. A study of the application to diffraction of light by a slit or a hole in a screen is described.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Jancewicz: 1988, ‘Multivectors and Clifford Algebra in Electrodynamics’, World Scientific, Singapore.

    MATH  Google Scholar 

  2. M. Riesz: 1958. ‘Clifford Numbers and Spinors’. University of Maryland, Kluwer, Dordrecht, 1993.

    MATH  Google Scholar 

  3. W. E. Baylis: 1993, ‘Electrons, photons, and spinors in the Pauli algebra’ in Z. Oziewicz et. al. (eds.): ‘Spinors, Twistors, Clifford Algebras and Quantum Deformations’, Kluwer, Dordrecht, 97–108.

    Chapter  Google Scholar 

  4. W. R. Hamilton: 1853. ‘On the geometrical interpretation of some of results obtained by calculation with biquaternions’, Proc. Roy. Irish Acad. 1, 388–390.

    Google Scholar 

  5. K. Imaeda: 1957, ‘Contribution to the quaternion formulation of classical electrodynamics’, Bulletin of Dept. Art and Education 8, Yamanashi Unversity, 131–139.

    Google Scholar 

  6. K. Imaeda: 1976, ‘A new formulation of classical electrodynamics’, Nuovo Cimento, 32, 138–162.

    Article  MathSciNet  Google Scholar 

  7. K. Imaeda: 1950, ‘Linearization of Minkowski space and five-dimensional space’, Prog. Theor. Phys. 5, 133–135.

    Article  MathSciNet  Google Scholar 

  8. K. Imaeda: 1951, ‘Study of field equations and spaces by means of hypercomplex numbers’, (in Japanese), Bulletin of Dept. Art and Education, 2, Yamanashi University, 111–118.

    Google Scholar 

  9. R. Fueter: 1935, ‘Die Funktionentheorie der Differentialgleichungen Δu = 0 und ΔΔu = 0 mit vier reellen Variablen’, Comm. Math. Helv. 7, 307–330.

    Article  MathSciNet  Google Scholar 

  10. R. Fueter: 1936, ‘Über die Analytischen Darstellung der regulären Funktionen einer Quaternionenvariablen’, Comm, Math. Helv. 8, 371–378.

    Article  MathSciNet  Google Scholar 

  11. K. Imaeda: 1983, ‘Quaternionic formulation of classical electrodynamics and theory of functions of a biquaternion variable’, Report FPL, Okayama University of Science. (unpublished)

    Google Scholar 

  12. Von M. Eichler: 1939, ‘Allgemeine Integration einiger partiellier Differentialgleichungen der Mathematischen Physik durch Quaternionenfunktionen.’ Comm. Math. Helv. Vol. 11, 212–224.

    Article  Google Scholar 

  13. K. Imaeda: 1981, ‘Solutions of Maxwell’s equations by means of regular functions of a biquaternion variable’, Bull. Okayama Univ. Science, 17A, 25–33.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Imaeda, K. (1995). Biquaternionic Formulation of Maxwell’s Equations and their Solutions. In: Ablamowicz, R., Lounesto, P. (eds) Clifford Algebras and Spinor Structures. Mathematics and Its Applications, vol 321. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8422-7_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-8422-7_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4525-6

  • Online ISBN: 978-94-015-8422-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics