David A. Meyer
University of California, San Diego
Classical reversible lattice gas models have been generalized in (at least) two directions. First, quantum lattice gas models evolve unitarily rather than deterministically, and in different continuum limits become multi-particle Schroedinger or Dirac equations. Second, dynamical geometry “lattice” gas models include local, reversible, reconfigurations of the underlying discrete space, coupled to the local particle content. In the present work we investigate the possibility of combining these two generalizations into models of quantum particles coupled to an underlying dynamical discrete space. The resulting states of the system include quantum superpositions of classical states with different geometries. As a toy model of quantum geometry, it is natural to insist that some version of general covariance apply; we show that this restricts the models, but not to the point of nonexistence.