  We study the problem of the cosmological constant in the context of the
multiverse in Lorentzian spacetime, and show that the cosmological constant
will vanish in the future. This sort of argument was started from Coleman in
1989, and he argued that the Euclidean wormholes make the multiverse partition
a superposition of various values of the cosmological constant $\Lambda$, which
has a sharp peak at $\Lambda=0$. However, the implication of the Euclidean
analysis to our Lorentzian spacetime is unclear. With this motivation, we
analyze the quantum state of the multiverse in Lorentzian spacetime by the WKB
method, and calculate the density matrix of our universe by tracing out the
other universes. Our result predicts vanishing cosmological constant. While
Coleman obtained the enhancement at $\Lambda=0$ through the action itself, in
our Lorentzian analysis the similar enhancement arises from the front factor of
$e^{iS}$ in the universe wave function, which is in the next leading order in
the WKB approximation.
