We give an example of a purely bosonic model—a rotor model on the 3D cubic lattice—whose low energy excitations behave like massless U(1) gauge bosons and massless Dirac fermions. This model can be viewed as a “quantum ether;” a medium that gives rise to both photons and electrons. It illustrates a general mechanism for the emergence of gauge bosons and fermions known as “string-net condensation.” Other, more complex, string-net condensed models can have excitations that behave like gluons, quarks and other particles in the standard model. This suggests that photons, electrons and other elementary particles may have a unified origin: string-net condensation in our vacuum.

• Received 9 July 2005

DOI:https://doi.org/10.1103/PhysRevB.73.035122