Weyl's Lagrangian in teleparallel form

Details Weyl's Lagrangian in teleparallel form Weyl's Lagrangian in teleparallel form

2009-01-08

arxiv.org/abs/0901.1070v1

J. Math. Phys. 50:102501,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1063/1.3204975

The main result of the paper is a new representation for 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 this gives the Weyl Lagrangian up to a nonlinear change of dynamical variable. 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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