  Quantum spin and quantum link models provide an unconventional regularization
of field theory in which classical fields arise via dimensional reduction of
discrete variables. This D-theory regularization leads to the same continuum
theories as the conventional approach. We show this by deriving the low-energy
effective Lagrangians of D-theory models using coherent state path integral
techniques. We illustrate our method for the $(2+1)$-d Heisenberg quantum spin
model which is the D-theory regularization of the 2-d O(3) model. Similarly, we
prove that in the continuum limit a $(2+1)$-d quantum spin model with
$SU(N)_L\times SU(N)_R\times U(1)_{L=R}$ symmetry is equivalent to the 2-d
principal chiral model. Finally, we show that $(4+1)$-d SU(N) quantum link
models reduce to ordinary 4-d Yang-Mills theory.
