2005/10/21 by Baker, John M.
#FOS: Physical sciences #Other Condensed Matter (cond-mat.other)
paper · doi:10.48550/arxiv.cond-mat/0510579
Starting from a model of an elastic medium, we derive equations of motion that are identical in form to Dirac's equation for a spin 1/2 particle with mass, coupled to electromagnetic and gravitational interactions. The mass and electromagnetic terms are not added by hand but emerge naturally from the formalism. A two dimensional version of this equation is derived by starting with a model in three dimensions and deriving equations for the dynamics of the lowest Fourier modes assuming one dimension to be periodic. Generalizations to higher dimensions are discussed.