Emergent spin

Authors :: Creutz, Michael
Publication Year :: 2013
Abstract: Quantum mechanics and relativity in the continuum imply the well known spin-statistics connection. However for particles hopping on a lattice, there is no such constraint. If a lattice model yields a relativistic field theory in a continuum limit, this constraint must "emerge" for physical excitations. We discuss a few models where a spin-less fermion hopping on a lattice gives excitations which satisfy the continuum Dirac equation. This includes such well known systems such as graphene and staggered fermions.<br />Comment: 14 pages, 3 figures. Revision has the four dimensional discussion substantially rewritten