Teleparallel model for the neutrino
Abstract
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 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 Griffiths and Newing.
 Publication:

Physical Review D
 Pub Date:
 January 2007
 DOI:
 10.1103/PhysRevD.75.025006
 arXiv:
 arXiv:grqc/0604011
 Bibcode:
 2007PhRvD..75b5006V
 Keywords:

 04.50.+h;
 11.15.q;
 14.60.Lm;
 Gravity in more than four dimensions KaluzaKlein theory unified field theories;
 alternative theories of gravity;
 Gauge field theories;
 Ordinary neutrinos (nuW bosons;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematics  Differential Geometry
 EPrint:
 4 pages, REVTeX