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Weyl's Lagrangian in teleparallel form

J. Math. Phys. 50, 102501 (2009); doi:10.1063/1.3204975

Published 20 October 2009

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James Burnett and Dmitri Vassiliev
Department of Mathematics and Institute of Origins, University College London, Gower Street, London WC1E 6BT, United Kingdom
The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable — the coframe (an orthonormal tetrad of covector fields). We show that when written in terms of this dynamical variable, the Weyl Lagrangian becomes remarkably simple: it is the wedge product of axial torsion of the teleparallel connection with a teleparallel lightlike element of the coframe. We also examine the issues of U(1)-invariance and conformal invariance. Examination of the latter motivates us to introduce a positive scalar field (equivalent to a density) as an additional dynamical variable; this makes conformal invariance self-evident. ©2009 American Institute of Physics
History: Received 8 January 2009; accepted 23 July 2009; published 20 October 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/102501/1
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KEYWORDS and PACS

Keywords
PACS
  • 11.30.Cp
    Lorentz and Poincaré invariance in particles and fields
  • 14.60.Lm
    Ordinary neutrinos (νe, νμ, ντ)
  • YEAR: 2009

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ISSN:
0022-2488 (print)   1089-7658 (online)
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REFERENCES (36)
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  1. D. Vassiliev, Phys. Rev. D 75, 025006 (2007).
  2. E. Cartan and A. Einstein, Letters on Absolute Parallelism (Princeton University Press, Princeton, 1979).
  3. A. Unzicker and T. Case (unpublished).
  4. T. Sauer, Hist. Math. 33, 399 (2006).
  5. E. Cosserat and F. Cosserat, Théorie des Corps Déformables, Librairie Scientifique A. Hermann et Fils, Paris, 1909. Reprinted by Cornell University Library.
  6. J. M. Ball, A. Taheri, and M. Winter, Calculus Var. Partial Differ. Equ. 14, 1 (2002).
  7. C. Liu and F. Lin, J. Partial Differ. Equ. 14, 289 (2001).
  8. J. M. Ball, London Analysis and Probability Seminar, 25 October 2007 (unpublished).
  9. É. Cartan, C. R. Acad. Sci. (Paris) 174, 593 (1922).
  10. H. F. M. Goenner, Living Rev. Relativ. 7, 2 (2004).
  11. F. W. Hehl and Yu. N. Obukhov, Ann. Fond. Louis Broglie 32, 157 (2007).
  12. A. D. King and D. Vassiliev, Class. Quantum Grav. 18, 2317 (2001).
  13. D. Vassiliev, Gen. Relativ. Gravit. 34, 1239 (2002).
  14. D. Vassiliev, Ann. Phys. (Leipzig) 14, 231 (2005).
  15. V. Pasic and D. Vassiliev, Class. Quantum Grav. 22, 3961 (2005).
  16. E. T. Newman and R. Penrose, J. Math. Phys. 3, 566 (1962).
  17. A. L. Besse, Einstein Manifolds (Springer-Verlag, Berlin, 1987).
  18. The group B2 can, in fact, be characterized as the nontrivial Abelian subgroup of the Lorentz group. See Appendix B in Ref. 1, for details.
  19. A. Dimakis and F. Müller-Hoissen, J. Math. Phys. 26, 1040 (1985).
  20. A. Dimakis and F. Müller-Hoissen, Phys. Lett. A 142, 73 (1989).
  21. A. Dimakis and F. Müller-Hoissen, Class. Quantum Grav. 7, 283 (1990).
  22. J. B. Griffiths and R. A. Newing, J. Phys. A 3, 269 (1970).
  23. D. Vassiliev, in Proceedings of the 11th Marcel Grossmann Meeting on General Relativity, edited by H. Kleinert and R. T. Jantzen (World Scientific, Singapore, 2008), Pt. B, pp. 1245–1247.
  24. J. Burnett, O. Chervova, and D. Vassiliev, in Analysis, Partial Differential Equations and Applications, The Vladimir Maz'ya Anniversary Volume, Series Operator Theory: Advances and Applications Vol. 193, edited by A. Cialdea, F. Lanzara, and P. E. Ricci (Birkhäuser, Basel, Switzerland, 2009), pp. 15–29.
  25. O. Chervova and D. Vassiliev (unpublished).
  26. J. Frauendiener, Class. Quantum Grav. 8, 1881 (1991).
  27. J. M. Nester, J. Math. Phys. 33, 910 (1992).
  28. G. Y. Chee, Phys. Rev. D 68, 044006 (2003).
  29. V. Pelykh, Phys. Rev. D 72, 108502 (2005).
  30. F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne'eman, Phys. Rep. 258, 1 (1995).
  31. F. W. Hehl, J. Nitsch, and P. von der Heyde, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 1, pp. 329–355.
  32. F. Gronwald and F. W. Hehl, Quantum gravity (Erice, 1995)
    33. The Science and Culture Series—Physics (World Scientific, River Edge, NJ, 1996), Vol. 10, pp. 148–198.
  33. U. Muench, F. Gronwald, and F. W. Hehl, Gen. Relativ. Gravit. 30, 933 (1998).
  34. V. C. de Andrade, L. C. T. Guillen, and J. G. Pereira, in Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, edited by H. Kleinert and R. T. Jantzen (World Scientific, Singapore, 2002).
  35. M. Blagojević, Gravitation and Gauge Symmetries, Series in High Energy Physics, Cosmology and Gravitation (IOP, Bristol, 2002).
  36. Yu. N. Obukhov and J. G. Pereira, Phys. Rev. D 67, 044016 (2003).

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