Massless Dirac equation as a special case of Cosserat elasticity

Details Massless Dirac equation as a special case of Cosserat elasticity Massless Dirac equation as a special case of Cosserat elasticity

2009-02-07

arxiv.org/abs/0902.1268v1

Journal of the Association of Arab Universities for Basic and Applied Sciences, 2009, vol. 7, p. 25-42. (Proceedings of the In

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Submitted to the proceedings of the International Conference on Recent Trends in Mathematical Sciences, Bahrain, 10-12 Novembe

Scientific paper

We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework is a special case of the so-called Cosserat theory of elasticity. Rotations of points of the continuum are described by attaching to each point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory we choose a coframe and a density. We write down a potential energy which is conformally invariant and then incorporate time in the standard Newtonian way, by subtracting kinetic energy. Finally, we rewrite the resulting nonlinear variational problem in terms of an unknown spinor field. We look for quasi-stationary solutions, i.e. solutions that harmonically oscillate in time. We prove that in the quasi-stationary setting our model is equivalent to a pair of massless Dirac equations. The crucial element of the proof is the observation that our Lagrangian admits a factorisation.

Affiliated with

Also associated with

No associations

Rating

Massless Dirac equation as a special case of Cosserat elasticity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Massless Dirac equation as a special case of Cosserat elasticity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Massless Dirac equation as a special case of Cosserat elasticity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-312231