What are the interactions in quantum glasses?

The form of the low-temperature interactions between defects in neutral glasses is reconsidered. We analyze the case where the defects can be modeled either as simple two-level tunneling systems, or tunneling rotational impurities. The coupling to strain fields is determined up to second order in the displacement field. It is shown that the linear coupling generates not only the usual 1/r³ Ising-like interaction between the rotational tunneling defect modes, which causes them to freeze around a temperature T _G, but also a random field term. At lower temperatures the inversion symmetric tunneling modes are still active - however, the coupling of these to the frozen rotational modes, now via the second-order coupling to phonons, generates another random field term acting on the inversion symmetric modes (as well as shorter-range 1/r⁵ interactions between them). Detailed expressions for all these couplings are given.