The g-based Jordan algebra and Lie algebra formulations of the Maxwell equations

Journal of Mechanics

Volumn 20, Issue 4, 2004, Pages 285-296

  Liu, Chein Shan ^a  

^a NATIONAL TAIWAN OCEAN UNIVERSITY   (Taiwan)

Author keywords

Jordan algebra; Lie algebra; Lorentz gauge condition; Maxwell equations; Quaternions; Wave equations

Indexed keywords

ALGEBRA; ELECTRIC FIELDS; ELECTRODYNAMICS; MAGNETIC FIELDS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; SET THEORY; VECTORS; WAVE EQUATIONS;

JORDAN ALGEBRA; LIE ALGEBRA; LORENTZ GAUGE CONDITIONS; QUATERNIONS;

MAXWELL EQUATIONS;

EID: 11244264013     PISSN: 17277191     EISSN: None     Source Type: Journal    
DOI: 10.1017/S1727719100003518     Document Type: Article

References (20)

1. Flanders, H., Differential Forms: With Applications to the Physical Sciences, Academic, New York (1963).
2. Baez, J. and Muniain, J. P., Gauge Fields, Knots and Gravity, World Scientific, Singapore (1994).
3. Jack, P. M., "Physical Space as a Quaternion Structure, I: Maxwell Equations, A Brief Note," http://arxiv.org/PS_cache/math-ph/pdf/0307/ 030703 8.pdf (2003).
4. Sweetser, D. B., "Doing Physics with Quaternions," http://world.std.com/~sweetser/quaternions/ps/bookpdf(2003).
5. Hestenes, D., Space-Time Algebra, Gordon and Breach, New York (1966).
6. Scott, J., "Complex Four-Vector Algebra," http://pws.prserv.net/jonathan_scott/physics/cfv.pdf (1998).
7. Misner, C. W., Thorne, K. S., Wheeler, J. A., Gravitation, W. H. Freeman and Company, San Francisco (1973).
8. Jackson, J. D., Classical Electrodynamics, 3rd Ed., Wiley, New York (1999).
9. Baylis, W. E., Electrodynamics, a Modern Geometric Approach, Birkhäuser, Boston (1998).
10. Gsponer, A. and Hurni, J. P., "Comment on Formulating and Generalizing Dirac's, Proca's, and Maxwell's Equations with Biquaternions or Clifford Numbers," Found. Phys. Lett., 14, pp. 77-85 (2001).
11. Gsponer, A., "On the 'Equivalence' of the Maxwell and Dirac Equations," Int. J. Theor. Phys., 41, pp. 689-694 (2002).
12. Waser, A., "Quaternions in Electrodynamics," http://www.aw-verlag.ch/Documents/ QuaternionsInElectrodynamicsEN02.pdf (2000).
13. Okubo, S., Introduction to Octonion and Other Non-Associative Algebras in Physics, Cambridge University, New York (1995).
14. Liu, C.-S., "Applications of the Jordan and Lie Algebras for Some Dynamical Systems Having Internal Symmetries," Int. J. Appl. Math., 8, pp. 209-240 (2002).
15. Yaglom, I. M., Complex Numbers in Geometry, Academic, New York (1968).
16. Liu, C.-S., "A Jordan Algebra and Dynamic System with Associator as Vector Field," Int. J. Non-Linear Mech., 35, pp. 421-429 (2000).
17. Schafer, R. D., An Introduction to Nonassociative Algebra, Dover, New York (1995).
18. Liu, C.-S., "The g-Based Jordan Algebra and Lie Algebra with Application to the Model of Visco-Elastoplasticity," J. Marine Sci. Tech., 9, pp. 1-13 (2001).
19. Hestenes, D., "Spacetime Physics with Geometric Algebra," Am. J. Phys., 71, pp. 691-714 (2003).
20. Hong, H.-K. and Liu, C.-S., "Some Physical Models with Minkowski Spacetime Structure and Lorentz Group Symmetry," Int. J. Non-Linear Mech., 36, pp. 1075-1084 (2001).