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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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