A teleparallel representation of the Weyl Lagrangian

Details A teleparallel representation of the Weyl Lagrangian A teleparallel representation of the Weyl Lagrangian

2007-02-03

arxiv.org/abs/gr-qc/0702020v1

Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity (in 3 volumes, editors H.Kleinert and R.T.Jantzen,

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Submitted to the Proceedings of the Eleventh Marcel Grossmann Meeting

Scientific paper

The main result of the paper is a new representation of the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show that variation of the resulting action with respect to the coframe produces the Weyl equation. The advantage of our approach is that it does not require the use of spinors, Pauli matrices or covariant differentiation. The only geometric concepts we use are those of a metric, differential form, wedge product and exterior derivative. Our result assigns a variational meaning to the tetrad representation of the Weyl equation suggested by J.B.Griffiths and R.A.Newing.

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