# 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.

- Authors:

- Department of Mathematics, University College London, Gower Street, London WC1E 6BT (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 21010919

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.025006; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; LAGRANGIAN FUNCTION; NEUTRINOS; PAULI SPIN OPERATORS; QUANTUM FIELD THEORY; SPINORS; VARIATIONAL METHODS; VARIATIONS; WEYL UNIFIED THEORY

### Citation Formats

```
Vassiliev, Dmitri.
```*Teleparallel model for the neutrino*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.025006.

```
Vassiliev, Dmitri.
```*Teleparallel model for the neutrino*. United States. doi:10.1103/PHYSREVD.75.025006.

```
Vassiliev, Dmitri. Mon .
"Teleparallel model for the neutrino". United States.
doi:10.1103/PHYSREVD.75.025006.
```

```
@article{osti_21010919,
```

title = {Teleparallel model for the neutrino},

author = {Vassiliev, Dmitri},

abstractNote = {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.},

doi = {10.1103/PHYSREVD.75.025006},

journal = {Physical Review. D, Particles Fields},

number = 2,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}