Dynamical lattice theory

A version of lattice gauge theory is presented in which the shape of the lattice is not assumed at the outset but is a consequence of the dynamics. Other related features which are not specified a priori include the internal and space-time symmetry groups and the dimensionality of space-time. The theory possesses a much larger invariance group than the usual gauge group on a lattice, and has associated with it an integer $k_0$ analogous to the topological quantum numer of quantum chromodynamics. Families of semiclassical solutions are found which are labeled by $k_0$ and a second integer $x$, but the analysis is not carried far enough to determine which space-time and internal symmetry groups characterize the lowest-lying states of the theory.