GLASS - ELEMENTARY EXCITATIONS AND GEOMETRY - FROM BONDS TO TUNNELINGMODES

Ground-state and elementary excitations (tunnelling modes) in glass ar e obtained from an analysis of its symmetry: a local gauge invariance. Glass is represented as a discrete fibre bundle. The base space is a continuous random network with tetravalent silicon atoms as vertices a nd chemical bonds as edges. The connection is given by the elasticity of the network. The bundle is non-trivial, and the elastic connection is entangled in one of two ways around odd rings in the network. To re store gauge invariance, tunnelling must occur between the two possible configurations. Entanglement, and elementary excitations are labelled by permutations of the covalent bonds incident on an atom.