Abstract
The use of complexified quaternions andi-complex geometry in formulating the Dirac equationallows us to give interesting geometric interpretationshidden in the conventional matrix-basedapproach.
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REFERENCES
Adler, S. L. (1995). Quaternionic Quantum Mechanics and Quantum Fields, Oxford University Press, Oxford.
Baylis, W. E. (1997). In The Theory of the Electron, Advances in Applied Clifford Algebras 7(S), J. Keller and Z. Oziewicz, eds., Universidad Nacional Autónoma, Mexico.
Bjorken, J. D., and Drell, S. D. (1985). Relativistic Quantum Mechanics, McGraw-Hill, New York.
Davies, A. J. (1990). Physical Review D, 41, 2628.
De Leo, S. (1996). International Journal of Modern Physics A, 11, 3073.
De Leo, S., and Rodrigues, W. A. (1997). International Journal of Theoretical Physics, 36, 2725.
De Leo, S., and Rodrigues, W. A. Quaternionic electron theory: Dirac's Equation, International Journal of Theoretical Physics, to appear.
Feynman, R. P. (1975). The Feynman Lectures on Physics, Vol. 1, Part 1, Addison-Wesley, Reading, Massachusetts.
Hestenes, D. (1966). Space-Time Algebra, Gordon and Breach, New York.
Hestenes, D. (1967a). Journal of Mathematical Physics, 8, 798.
Hestenes, D. (1967b). Journal of Mathematical Physics, 8, 809.
Hestenes, D. (1991). Foundations of Physics, 20, 1213.
Hestenes, D., and Gurtler, R. (1971). American Journal of Physics, 39, 1028.
Itzytson, S., and Zuber, J. B. (1985). Quantum Field Theory, McGraw-Hill, New York.
Rodrigues, W. A., de Souza, Q. A. G., and Vaz, J. (1995). In Clifford Algebras and Spinor Structures, V. Ablamowicz and P. Lounesto, eds., Kluwer, Dordrecht, p. 177.
Rotelli, P. (1989). Modern Physics Letters A, 4, 933.
Ward, J. P. (1997). Quaternions and Cayley Numbers, Kluwer, Dordrecht.
Zeni, J. R. (1994). In Gravitation: The Space-Time Structure, P. Letelier and W. A. Rodrigues, eds., World Scientific, Singapore, p. 544.
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Leo, S.D., Rodrigues, W.A. Quaternionic Electron Theory: Geometry, Algebra, and Dirac's Spinors. International Journal of Theoretical Physics 37, 1707–1720 (1998). https://doi.org/10.1023/A:1026692508708
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DOI: https://doi.org/10.1023/A:1026692508708