  The validity of the Coleman mechanism, which automatically tunes the
fundamental constants, is examined in two-dimensional and four-dimensional
quantum gravity theories. First, we consider two-dimensional Euclidean quantum
gravity on orientable closed manifolds coupled to conformal matter of central
charge $c \leq1$. The proper time Hamiltonian of this system is known to be
written as a field theory of noncritical strings, which can also be viewed as a
third quantization in two dimensions. By directly counting the number of random
surfaces with various topologies, we find that the contribution of the baby
universes is too small to realize the Coleman mechanism. Next, we consider
four-dimensional Lorentzian gravity. Based on the difference between the
creation of the mother universe from nothing and the annihilation of the mother
universe into nothing, we introduce a non-Hermitian effective Hamiltonian for
the multiverse. We show that Coleman's idea is satisfied in this model and that
the cosmological constant is tuned to be nearly zero. Potential implications
for phenomenology are also discussed.
