Why does the geometric product simplify the equations of physics?

International Journal of Theoretical Physics

Volumn 41, Issue 10, 2002, Pages 1841-1855

  Friedman, Yaakov ^a   Gofman, Yuriy ^a  

^a JERUSALEM COLLEGE OF TECHNOLOGY   (Israel)

Author keywords

Bounded symmetric domain; Geometric product; Special relativity; Spin factor

Indexed keywords

EID: 0036430723     PISSN: 00207748     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021048722241     Document Type: Article

References (17)

1. Baylis, W. E. (ed.). (1996). Clifford (Geometric) Algebras with Applications to Physics, Mathematics and Engineering, Birkhouser, Boston.
2. Dang, T. and Friedman, Y. (1987). Classification of JBW*-triples and applications. Mathematical Scand inavian 61, 292-330.
3. Einstein, A. (1905). Zur Elektrodynamik bewegter Körper. Annalen der Physik 17, 891.
4. Eisenberg, L. J. (1967). Necessity of the linearity of relativistic transformations between inertial sytems. American Journal of Physics 35, 649.
5. Friedman, Y. (1994). Bounded symmetric domains and the JB*-triple structure in physics (Jordan Algebras). In Proceedings of the Oberwolfach Conference 1992, W. Kaup, K. McCrimmon, and H. Petersson, eds., de Gruyter, Berlin, pp. 61-82.
6. 3 and special relativity. Foundation of Physics Letters 5, 337-354.
7. Friedman, Y. and Russo, B. (1986). The Gelfand-Naimark Theorem for JB* triples. Duke Mathematical Journal 53, 139-148.
8. Friedman, Y. and Russo, B. (1992). Geometry of the dual ball of the spin factor. Proceedings of the London Mathematical Society 65, 142-174.
9. Friedman, Y. and Russo, B. (1993). Classification of atomic facially symmetric spaces. Canadian Journal of Mathematics 45(1), 33-87.
10. Friedman, Y. and Russo, B. (2001). A new approach to spinors and some representation of the Lorentz group on them. Foundation of Physics 31(12), 1733-1766.
11. Günaydin, M. (1980). Quadratic Jordan formulation of quantum mechanics and construction of Lie (super) algebras from Jorda (super) algebras, VIII Internat. Coloq. on Group Theoretical Methods in Physics, Kiryat Anavim, Israel, 1979. Annales Israel Physics Society 3, 279-296.
12. Hestenes, D. and Sobczyk, G. (1984). Clifford Algebra to Geometric Calculus, Kluwer Academic, Dordrecht.
13. Kaup, W. (1983). A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces. Mathematical Zeitschrift für 183, 503-529.
14. Lasenby, J., Lasenby, A. N., and Doran, C. J. L. (2000). A unified mathematical language for physics and engineering in the 21st century. Philosophical Transactions of the Royal Society of London A 358, 21-39.
15. Loos, O. (1977). Bounded Symmetric Domains and Jordan Pairs, University of California, Irvine.
16. Schwartz, H. M. (1984). Deduction of the general Lorentz transformations from a set of necessary assumpfions. American Journal of Physics 52(4), 346-350.
17. Ungar, A.A. (2001). Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession, Kluwer Academic, Dordrecht. Fundamental Theories of Physics, Vol. 117.