The relation between Maxwell, Dirac and the Seiberg-Witten equations

International Journal of Mathematics and Mathematical Sciences

Volumn 2003, Issue 43, 2003, Pages 2707-2734

  Rodrigues Jr , Waldyr A ^a  

^a NONE

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[No Author keywords available]

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EID: 3543091492     PISSN: 01611712     EISSN: None     Source Type: Journal    
DOI: 10.1155/S0161171203210218     Document Type: Article

References (40)

1. A. A. Campolattaro, New spinor representation of Maxwell equations. II. Algebraic properties, Internat. J. Theoret. Phys. 19 (1980), no. 2, 127-138. MathSciNet. Zentralblatt für Mathematik.
2. A. A. Campolattaro, New spinor representation of Maxwell's equations. I. Generalities, Internat. J. Theoret. Phys. 19 (1980), no. 2, 99-126. MathSciNet. Zentralblatt für Mathematik.
3. A. A. Campolattaro, Generalized Maxwell equations and quantum mechanics. I. Dirac equation for the free electron, Internat. J. Theoret. Phys. 29 (1990), no. 2, 141-155. MathSciNet.
4. A. A. Campolattaro, Generalized Maxwell equations and quantum mechanics. II: Generalized Dirac equation, Internat. J. Theoret. Phys. 29 (1990), no. 5, 477-482. Zentralblatt für Mathematik.
5. A. A. Campolattaro, Classical electrodynamics and relativistic quantum mechanics, Adv. Appl. Clifford Algebras 7 (1997), suppl., 167-173. MathSciNet.
6. M. Chown, Double or quit, New Scientist 168 (2000), no. 2260, 24-27.
7. J. P. Crawford, On the algebra of Dirac bispinor densities: factorization and inversion theorems, J. Math. Phys. 26 (1985), no. 7, 1439-1441. CrossRef. MathSciNet.
8. E. C. de Oliveira and W. A. Rodrigues Jr., Superluminal electromagnetic waves in free space, Ann. Physik 7 (1998), 654-659. Zentralblatt für Mathematik.
9. E. C. de Oliveira and W. A. Rodrigues Jr., Finite energy superluminal solutions of Maxwell equations, Phys. Lett. A 291 (2001), no. 6, 367-370. CrossRef. MathSciNet. Zentralblatt für Mathematik.
10. E. C. de Oliveira, W. A. Rodrigues Jr., D. S. Thober, and A. L. Xavier Jr., Thoughtful comments on: "Bessel beams and signal propagation", Phys. Lett. A 284 (2001), no. 6, 296-303. CrossRef. MathSciNet. Zentralblatt für Mathematik.
11. Q. A. G. de Souza and W. A. Rodrigues Jr., The Dirac operator and the structure of Riemann-Cartan-Weyl spaces, Gravitation: The Spacetime Structure (Águas De Lindóia, 1993) (P. S. Letelier and W. A. Rodrigues Jr., eds.), World Scientific Publishing, New Jersey, 1994, pp. 179-212. MathSciNet. Zentralblatt für Mathematik.
12. V. L. Figueiredo, E. C. de Oliveira, and W. A. Rodrigues Jr., Clifford algebras and the hidden geometrical nature of spinors, Algebras Groups Geom. 7 (1990), no. 2, 153-198. MathSciNet. Zentralblatt für Mathematik.
13. V. L. Figueiredo, E. C. de Oliveira, and W. A. Rodrigues Jr., Covariant, algebraic, and operator spinors, Internat. J. Theoret. Phys. 29 (1990), no. 4, 371-395. MathSciNet. Zentralblatt für Mathematik.
14. A. Gsponer, On the "equivalence" of the Maxwell and Dirac equations, Internat. J. Theoret. Phys. 41 (2002), no. 4, 689-694. CrossRef. MathSciNet. Zentralblatt für Mathematik.
15. F. Gürsey, Contribution to the quaternion formalism in special relativity, Rev. Fac. Sci. Univ. Istanbul. Sér. A. 20 (1956), 149-171. MathSciNet.
16. G. Lochak, Wave equation for a magnetic monopole, Internat. J. Theoret. Phys. 24 (1985), no. 10, 1019-1050. MathSciNet.
17. P. Lounesto, Clifford algebras and Hestenes spinors, Found. Phys. 23 (1993), no. 9, 1203-1237. MathSciNet.
18. P. Lounesto, Clifford algebras, relativity and quantum mechanics, Gravitation: the Spacetime Structure (Águas de Lindóia, 1993) (P. S. Letelier and W. A. Rodrigues Jr., eds.), World Scientific Publishing, New Jersey, 1994, pp. 50-81. MathSciNet. Zentralblatt für Mathematik.
19. A. Maia Jr., E. Recami, W. A. Rodrigues Jr., and M. A. F. Rosa, Magnetic monopoles without string in the Kähler-Clifford algebra bundle: a geometrical interpretation, J. Math. Phys. 31 (1990), no. 2, 502-505. Cross Ref. MathSciNet. Zentralblatt für Mathematik.
20. J. E. Maiorino and W. A. Rodrigues Jr., What is superluminal wave motion?, Sci. and Tech. Mag. 2 (1999), no. 4, 1-179.
21. H. J. Maris, On the fission of elementary particles and the evidence for fractional electrons in liquid helium, J. Low Temp. Phys. 120 (2000), no. 3-4, 173-204. CrossRef.
22. R. A. Mosna and W. A. Rodrigues Jr., The bundles of algebraic and Dirac-Hestenes spinor fields, RP 57/02, IMECC-UIMICAMP, 2002.
23. G. L. Naber, Topology, Geometry, and Gauge Fields. Interactions, Applied Mathematical Sciences, vol. 141, Springer-Verlag, New York, 2000. MathSciNet. Zentralblatt für Mathematik.
24. C. Nash, Topology and physics - a historical essay, preprint, 1997, http://arxiv.org/abs/hep-th/9709135.
25. G. Y. Rainich, Electrodynamics in the general relativity theory, Trans. Amer. Math. Soc. 27 (1925), no. 1, 106-136. MathSciNet.
26. W. A. Rodrigues Jr., Algebraic and Dirac-Hestenes spinors and spinor fields, RP 56/02, IMECC-UNICAMP, 2002.
27. W. A. Rodrigues Jr. and E. C. de Oliveira, Dirac and Maxwell equations in the Clifford and spin-Clifford bundles, Internat. J. Theoret. Phys. 29 (1990), no. 4, 397-412. MathSciNet. Zentralblatt für Mathematik.
28. W. A. Rodrigues Jr. and Q. A. G. de Souza, The Clifford bundle and the nature of the gravitational field, Found. Phys. 23 (1993), no. 11, 1465-1490. MathSciNet.
29. W. A. Rodrigues Jr., Q. A. G. de Souza, and J. Vaz Jr., Spinor fields and superfields as equivalence classes of exterior algebra fields, Clifford Algebras and Spinor Structures (R. Ablamowicz and P. Lounesto, eds.), Math. Appl., vol. 321, Kluwer Academic Publishers, Dordrecht, 1995, pp. 177-198. MathSciNet. Zentralblatt für Mathematik.
30. W. A. Rodrigues Jr., Q. A. G. de Souza, J. Vaz Jr., and P. Lounesto, Dirac-Hestenes spinor fields on Riemann-Cartan manifolds, Internat. J. Theoret. Phys. 35 (1996), no. 9, 1849-1900. MathSciNet. Zentralblatt für Mathematik.
31. W. A. Rodrigues Jr. and J.-Y. Lu, On the existence of undistorted progressive waves (UPWs) of arbitrary speeds 0≤v<∞ in nature, Found. Phys. 27 (1997), no. 3, 435-508. MathSciNet.
32. W. A. Rodrigues Jr. and J. E. Maiorino, A unified theory for construction of arbitrary speeds (0≤v<∞) solutions of the relativistic wave equations, Random Oper. Stochastic Equations 4 (1996), no. 4, 355-400. MathSciNet. Zentralblatt für Mathematik.
33. W. A. Rodrigues Jr., D. S. Thober, and A. L. Xavier Jr., Causal explanation for observed superluminal behavior of microwave propagation in free space, Phys. Lett. A 284 (2001), no. 6, 217-224. CrossRef.
34. W. A. Rodrigues Jr. and J. Vaz Jr., Subluminal and superluminal solutions in vacuum of the Maxwell equations and the massless Dirac equation, Adv. Appl. Clifford Algebras 7 (1997), suppl., 457-466. MathSciNet.
35. W. A. Rodrigues Jr. and J. Vaz Jr., From electromagnetism to relativistic quantum mechanics, Found. Phys. 28 (1998), no. 5, 789-814. CrossRef. MathSciNet.
36. N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD, Nuclear Phys. B 431 (1994), no. 3, 484-550. CrossRef. MathSciNet.
37. A. L. Trovon de Carvalho and W. A. Rodrigues Jr., The non sequitur mathematics and physics of the "new electrodynamics" proposed by the AIAS group, Random Oper. Stochastic Equations 9 (2001), no. 2, 161-206. MathSciNet. Zentralblatt für Mathematik.
38. J. Vaz Jr., Clifford algebras and Witten's monopole equations, Geometry, Topology and Physics (Campinas, 1996) (B. N. Apanasov, S. B. Bradlow, W. A. Rodrigues Jr., and K. K. Uhlenbeck, eds.), de Gruyter, Berlin, 1997, pp. 277-300. MathSciNet. Zentralblatt für Mathematik.
39. J. Vaz Jr. and W. A. Rodrigues Jr., Equivalence of Dirac and Maxwell equations and quantum mechanics, Internat. J. Theoret. Phys. 32 (1993), no. 6, 945-959. MathSciNet. Zentralblatt für Mathematik.
40. J. Vaz Jr. and W. A. Rodrigues Jr., Maxwell and Dirac theories as an already unified theory, Adv. Appl. Clifford Algebras 7 (1997), suppl., 369-386. MathSciNet.