A 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 J.B.Griffiths and R.A.Newing.

4 pages, REVTeX

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Cited by in corpus (8)

• Rotational elasticity
• The stationary Weyl equation and Cosserat elasticity
• Modeling the electron with Cosserat elasticity
• Weyl's Lagrangian in teleparallel form
• The Einstein-Yang-Mills equations from Bianchi identities
• Massless Dirac equation as a special case of Cosserat elasticity
• Topological charges and quasi-charges in Absolute Parallelism
• Geometric Origin of Physical Constants in a Kaluza-Klein Tetrad Model