  We consider quantum rotors or Ising spins in a transverse field on a
$d$-dimensional lattice, with random, frustrating, short-range, exchange
interactions. The quantum dynamics are associated with a finite moment of
inertia for the rotors, and with the transverse field for the Ising spins. For
a suitable distribution of exchange constants, these models display spin glass
and quantum paramagnet phases and a zero temperature quantum transition between
them. An earlier exact solution for the critical properties of a model with
infinite-range interactions can be reproduced by minimization of a Landau
effective-action functional for the model in finite $d$ with short-range
interactions. The functional is expressed in terms of a composite spin field
which is bilocal in time. The mean-field phase diagram near the zero
temperature critical point is mapped out as a function of temperature, strength
of the quantum coupling, and applied fields. The spin glass ground state is
found to be replica symmetric, with replica symmetry breaking appearing only at
finite temperatures. Next we examine the consequences of fluctuations about
mean-field for the critical properties. Above $d=8$, and with certain
restrictions on the values of the Landau couplings, we find that the transition
is controlled by a Gaussian fixed point with mean-field critical exponents. For
couplings not attracted by the Gaussian fixed point above $d=8$, and for all
physical couplings below $d=8$, we find runaway renormalization group flows to
strong coupling. General scaling relations that should be valid even at the
strong coupling fixed point are proposed and compared with Monte Carlo
simulations.
