Abstract
The results of spin 1 symmetries of massless Dirac equation [21] are proved completely in the space of 4-component Dirac spinors on the basis of unitary operator in this space connecting this equation with the Maxwell equations containing gradient-like sources. Nonlocal representations of conformal group are found, which generate the transformations leaving the massless Dirac equation being invariant. The Maxwell equations with gradient-like sources are proved to be invariant with respect to fermionic representations of Poincaré and conformal groups and to be the kind of Maxwell equations with maximally symmetrical properties. Brief consideration of an application of these equations in physics is discussed.
Similar content being viewed by others
References
Darwin C. G.,Proc. Roy. Soc. London,A118 N780 (1928) 654–680.
Laporte O. and G. E. Uhlenbeck,Phys. Rev.,37 (1931) 1380–1397.
Oppenheimer J. R.,Phys. Rev.,38 (1931) 725–746.
Good R. H.,Phys. Rev.,105 N6 (1957) 1914–1919.
Moses H. E.,Nuovo Cimento Suppl.,7 (1958) 1–18.
Lomont J. S.,Phys. Rev.,111 N6 (1958) 1710–1716.
Borhgardt A. A.,Sov. Phys. JETP.,34 N2 (1958) 334–341.
Moses H. E.,Phys. Rev.,113 N6 (1959) 1670–1679, see de Analysis of this formulation in Keller J.,International Journal of Theoretical Physics,30 (2) (1991) 137–184; Keller J., “Spinosrs, Twistors, Clifford Algebras an Quantum Deformations”, Kluwer Academic Publishers, 189–196 1993
Mignani R., E. Recami and M. Baldo,Lett. Nuov. Cim.,11 N12 (1974) 572–586.
Sallhofer H.,Z. Naturforsch.,A33 (1978) 1379–1381.
Da Silveira A.,Z. Naturforsch.,A34 (1979) 646–647.
Campolattaro A.,Int. J. Theor. Phys.,19 (1980) 99–126.
Sallhofer H.,Z. Naturforsch.,A41 (1986) 1087–1088.
Ljolie K.,Fortschr. Phys.,36 N1 (1988) 9–32.
Sallhofer H.,Z. Naturforsch.,A46 (1991) 869–872.
Campolattaro A.,Int. J. Theor. Phys.,29 N2 (1990) 141–156.
Fushchich W. I., W. M. Shtelen and S. V. Spichak,J. Phys. A24 N8 (1991) 1683–1698.
Simulik V. M.,Theor. Math. Phys.,87 N1 (1991) 386–392.
Krivsky I. Yu. and V. M. Simulik, “Foundations of quantum electrodynamics in field strengths terms”, Naukova Dumka, Kiev, 1992, 288.
Krivsky I. Yu. and V. M. Simulik,Theor. Math. Phys.,90 N3 (1992) 265–276, 388–406.
Simulik V. M.,Z. Naturforsch.,A49 (1994) 1074–1076.
Simulik V. M. and I. Yu. Krivsky, An electrodynamical version of the hydrogen spectrum, in Proceedings. of the 28th European Group for Atomic Spectroscopy Conference, Graz., Austria, 1996, edited by L. Windholz, European Physical Society, Paris, 41–42.
Krivsky I. Yu. and V. M. Simulik,Advances in Applied Clifford Algebras,6 N2 (1996) 249–259.
Krivsky I. Yu. and V. M. Simulik,Proc. Acad. of Sci., Ukraine N8 (1996) 79–85.
Simulik V. M. and I. Yu. Krivsky, On a bosonic structure of electron and muon, in Proceedings. of the 29th European Group for Atomic Spectroscopy Conference, Berlin, (1997), edited by H.-D. Kronfeldt European Physical Society, Paris, 154–155.
Simulik V. M. and I. Yu. Krivsky, Theoretical derivation of atomic spectra in the classical electrodynamical model of atom, in Proceedings. of the 29th European Group for Atomic Spectroscopy Conference, Berlin, 1997, edited by H.-D. Kronfeldt European Physical Society, Paris, 198–199.
Simulik V. M.,Ukrainian Phys. Journ.,42 N4 (1997) 406–407.
Simulik V. M.,Ukranian Math. Journ.,49, N7 (1997) 958–970.
Ibragimov N. H.,Theor. Math. Phys.,1 N3 (1969) 350–359.
Fushchich W. I. and A. G. Nikitin, “Symmetries of Maxwell’s equations”, Naukova Dumka, Kiev, 1983, 200.
Simulik V. M. and I. Yu. Krivsky,Advances in Applied Clifford Algebras,7 N1 (1997) 25–34.
Keller J.,Advances in Applied Clifford Algebras,7 (S) 1997 3–26.
Vaz Jr. J. and W. A. Rodrigues Jr., On the Equivalence of Dirac and Maxwell Equations and Quantum Mechanics,Int. J. Theor. Phys.,32 (1993) 945–955.
Vaz Jr. J. and W. A. Rodrigues Jr., Maxwell and Dirac Equations as an Already Unitied Theory,Advances in Applied Clifford Algebras,7 (S), 1997 369–386.
Rodrigues Jr. W. A. and J. Vaz. Jr., From Electromagnetism to Relativistic Quantum Mechanics, in pressFound. Physics (special-issue dedicated to A. O. Barut), (1998).
Rodrigues Jr. W. A. and J. E. Maiorino, A Unified Theory for construction of Arbitrary Speeds 0≤v<∞ Solutions of the Relativistic Wave Equations,Random Oper. Stoch. Eq. 4, (1996) 355–400.
Rodrigues Jr. W. A. and J. Y. Lu, On the Existence of Undistorted Progressive Waves (UPWs) of Arbitrary Speeds 0<-v<∞ in Nature,Found. Phys.,27, (1997) 435–508.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Simulik, V.M., Krivsky, I.Y. Bosonic symmetries of the massless Dirac equation. AACA 8, 69–82 (1998). https://doi.org/10.1007/BF03041926
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF03041926