Lorentz symmetry from a random Hamiltonian

TL;DR

This paper investigates how Lorentz symmetry emerges from a random Hamiltonian by comparing energy eigenstate densities, showing that Lorentz symmetric dispersion relations better approximate a random Hamiltonian than non-symmetric ones.

Contribution

The study extends previous work by considering generalized dispersion relations and demonstrates that Lorentz symmetry is favored in approximating a random Hamiltonian.

Findings

Lorentz symmetric dispersion relations better match the density of states.

Non-symmetric dispersion relations provide a poorer approximation.

Lorentz symmetry emerges naturally in the random Hamiltonian framework.

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.