Modeling the electron with Cosserat elasticity

Details Modeling the electron with Cosserat elasticity Modeling the electron with Cosserat elasticity

2010-07-20

arxiv.org/abs/1007.3481v1

Physics

Mathematical Physics

Scientific paper

We suggest an alternative mathematical model for the electron in dimension 1+2. We think of our (1+2)-dimensional spacetime as an elastic continuum whose material points can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric 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 then add an extra (third) spatial dimension, extend our coframe and density into dimension 1+3, choose a conformally invariant Lagrangian proportional to axial torsion squared, roll up the extra dimension into a circle so as to incorporate mass and return to our original (1+2)-dimensional spacetime by separating out the extra coordinate. The main result of our paper is the theorem stating that our model is equivalent to the Dirac equation in dimension 1+2. In the process of analyzing our model we also establish an abstract result, identifying a class of nonlinear second order partial differential equations which reduce to pairs of linear first order equations.

Affiliated with

Also associated with

No associations

Rating

Modeling the electron with 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 Modeling the electron with Cosserat elasticity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modeling the electron with Cosserat elasticity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-126304