Spacetime as a Quantum Graph

A model of empty spacetime as a quantum hypercubical null lattice is presented. Particles are proposed to be defects in this lattice. The symmetries of these particles are inherited from the symmetries of the lattice which are here related to the groups of the standard model. To establish this relation, the permutation group S _4 is examined, and used to construct classical Lie groups by the method of coherent states. The theory is generalized to general spacetimes (called quantum graphs). An action principle for quantum graphs is sought which will result in a four dimensional universe. The relationship between this theory and particle masses and coupling constants is discussed.