Lorentz symmetry from a random Hamiltonian

Abstract

We match the density of energy eigenstates of a local field theory with that of a random Hamiltonian order by order in a Taylor expansion. In our previous work we assumed Lorentz symmetry of the field theory, which entered through the dispersion relation. Here we extend that work to consider a generalized dispersion relation and show that the Lorentz symmetric case is preferred, in that the Lorentz symmetric dispersion relation gives a better approximation to a random Hamiltonian than the other local dispersion relations we considered.Comment: 8 pages, 6 figures. V2: Final version accepted for publication in PRD. Discussion improved throughout, including clarification of the fact that we address our key questions only at the level of the dispersion relation. No change to our technical work or result