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Advances in Mathematical Physics
Volume 2011 (2011), Article ID 652126, 12 pages
http://dx.doi.org/10.1155/2011/652126
Research Article

Gauge and Lorentz Transformation Placed on the Same Foundation

1Loodus- ja Tehnoloogiateaduskond, Füüsika Instituut, Tartu Ülikool, Riia 142, 51014 Tartu, Estonia
2Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, 55099 Mainz, Germany

Received 25 March 2011; Accepted 14 April 2011

Academic Editor: H. Neidhardt

Copyright © 2011 Rein Saar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Weyl, “Eine neue Erweiterung der Relativitätstheorie,” Annalen der Physik, vol. 364, no. 10, pp. 101–133, 1919.
  2. W.-K. Tung, Group Theory in Physics, World Scientific, Philadelphia, Pa, USA, 1985.
  3. E. Wigner, “On unitary representations of the inhomogeneous Lorentz group,” Annals of Mathematics. Second Series, vol. 40, no. 1, pp. 149–204, 1939. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. E. Wigner, “On unitary representations of the inhomogeneous Lorentz group,” Nuclear Physics B (Proceedings Supplements), vol. 6, pp. 9–64, 1989, (Reprint from Annals of Mathematics, vol. 40, no. 1, pp. 149–204, 1939).
  5. V. Bargmann, “On unitary ray representations of continuous groups,” Annals of Mathematics. Second Series, vol. 59, pp. 1–46, 1954. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. C. Fronsdal, “Unitary irreducible representations of the Lorentz group,” Nuovo Cimento, vol. 113, pp. 1367–1374, 1959.
  7. R. Shaw, “Unitary representations of the inhomogeneous Lorentz group,” Nuovo Cimento, vol. 33, pp. 1074–1090, 1964. View at Zentralblatt MATH
  8. H. Joos, “Zur Darstellungstheorie der inhomogenen Lorentzgruppe als Grundlage quantenmechanischer Kinematik,” Fortschritte der Physik, vol. 10, no. 3, pp. 65–146, 1962.
  9. U. H. Niederer and L. O'Raifeartaigh, “Realizations of the Unitary Representations of the Inhomogeneous Space-Time Groups I. General Structure,” Fortschritte der Physik, vol. 22, no. 3, pp. 111–129, 1974.
  10. Y. Ohnuki, Unitary Representations of the Poincaré Group and Relativistic Wave Equations, World Scientific, Teaneck, NJ, USA, 1988.
  11. Y. S. Kim and M. E. Noz, Theory and Applications of the Poincaré Group, Fundamental Theories of Physics, D. Reidel, Dordrecht, The Netherlands, 1986.
  12. V. Bargmann and E. P. Wigner, “Group theoretical discussion of relativistic wave equations,” Proceedings of the National Academy of Sciences of the United States of America, vol. 34, pp. 211–223, 1948. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. E. M. Corson, Introduction to Tensors, Spinors, and Relativistic Wave Equations, Blackie and Sons, London, UK, 1953.
  14. D. L. Pursey, “General theory of covariant particle equations,” Annals of Physics, vol. 32, pp. 157–191, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. W.-K. Tung, “Relativistic wave equations and field theory for arbitrary spin,” Physical Review, vol. 156, no. 5, pp. 1385–1398, 1967. View at Publisher · View at Google Scholar
  16. A. S. Wightman, “Invariant wave equations: general theory and applications to the external field problem,” in Invariant wave equations (Proceedings of “Ettore Majorana” International School of Mathematical Physics of Erice, 1977), vol. 73 of Lecture Notes in Phys., pp. 1–101, Springer, Berlin, Germany, 1978.
  17. N. Giovannini, “Covariance group in the presence of external electromagnetic fields,” Helvetica Physica Acta, vol. 50, no. 3, pp. 337–348, 1977.
  18. A. Janner and E. Ascher, “Space-time symmetry of transverse electromagnetic plane waves,” Helvetica Physica Acta, vol. 43, pp. 296–303, 1970.
  19. H. J. Bhabha, “Relativistic wave equations for the elementary particles,” Reviews of Modern Physics, vol. 17, pp. 200–216, 1945. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. M. Fierz, “Über die relativistische Theorie kräftefreier Teilchen mit beliebigem Spin,” Helvetica Physica Acta, vol. 12, pp. 3–17, 1939.
  21. E. Wild, “On first order wave equations for elementary particles without subsidiary conditions,” Proceedings of the Royal Society. London. Series A, vol. 191, pp. 253–268, 1947. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. I. M. Gel'fand, R. A. Minlos, and Z. Y. Shapiro, Representations of Rotation and Lorentz Groups and Their Applications, Pergamon Press, Oxford, UK, 1963.
  23. M. A. Naimark, Linear Representations of the Lorentz Group, Pergamon Press, Oxford, UK, 1964.
  24. A. Charkrabarti, “Exact solution of the Dirac-Pauli equation for a class of fields: precession of polarization,” Il Nuovo Cimento A, vol. 56, no. 3, pp. 604–624, 1968. View at Publisher · View at Google Scholar · View at Scopus
  25. B. Beers and H. H. Nickle, “Algebraic solution for a Dirac electron in a plane-wave electromagnetic field,” Journal of Mathematical Physics, vol. 13, pp. 1592–1595, 1972. View at Publisher · View at Google Scholar
  26. R. Saar, R. K. Loide, I. Ots, and R. Tammelo, ““Dynamical” representation of the Poincaré algebra for higher-spin fields in interaction with plane waves,” Journal of Physics. A, vol. 32, no. 12, pp. 2499–2508, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. I. Ots, R. Saar, R. K. Loide, and H. Liivat, “"Dynamical" non-minimal higher-spin interaction and gyromagnetic ratio g = 2,” Europhysics Letters, vol. 56, no. 3, pp. 367–371, 2001. View at Publisher · View at Google Scholar · View at Scopus
  28. A. H. Taub, “A special method for solving the dirac equations,” Reviews of Modern Physics, vol. 21, no. 3, pp. 388–392, 1949. View at Publisher · View at Google Scholar
  29. D. M. Wolkow, “Über eine Klasse von Lösungen der Diracschen Gleichung,” Zeitschrift für Physik, vol. 94, no. 3-4, pp. 250–260, 1935. View at Publisher · View at Google Scholar
  30. N. D. Sen Gupta, “On the solution of the Dirac equation in the field of two beams of electromagnetic radiation,” Zeitschrift für Physik, vol. 200, no. 1, pp. 13–19, 1967. View at Publisher · View at Google Scholar
  31. M. Pardy, “Volkov solution for two laser beams and ITER,” International Journal of Theoretical Physics, vol. 45, no. 3, pp. 647–659, 2006. View at Publisher · View at Google Scholar
  32. J. J. Sakurai, Modern Quantum Mechanics, Addison-Wesley, Reading, Mass, USA, 1993.
  33. H. M. Fried, Basics of Functional Methods and Eikonal Models, Editions Frontières, Gif-sur-Yvette, France, 1990.
  34. R. Saar, S. Groote, H. Liivat, and I. Ots, ““Dynamical” interactions and gauge invariance,” http://arxiv.org/abs/0908.3761.